\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95+ \ \ \frac{\partial x_96}{\partial x_i\ }\ q_96\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95+ \ \frac{\partial x^{\prime i}}{\partial x^96\ }\ q^96\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95+ \ \ \frac{\partial x_96}{\partial x_i\ }\ q_96+ \ \ \frac{\partial x_97}{\partial x_i\ }\ q_97\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95+ \ \frac{\partial x^{\prime i}}{\partial x^96\ }\ q^96+ \ \frac{\partial x^{\prime i}}{\partial x^97\ }\ q^97\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95+ \ \ \frac{\partial x_96}{\partial x_i\ }\ q_96+ \ \ \frac{\partial x_97}{\partial x_i\ }\ q_97+ \ \ \frac{\partial x_98}{\partial x_i\ }\ q_98\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95+ \ \frac{\partial x^{\prime i}}{\partial x^96\ }\ q^96+ \ \frac{\partial x^{\prime i}}{\partial x^97\ }\ q^97+ \ \frac{\partial x^{\prime i}}{\partial x^98\ }\ q^98\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95+ \ \ \frac{\partial x_96}{\partial x_i\ }\ q_96+ \ \ \frac{\partial x_97}{\partial x_i\ }\ q_97+ \ \ \frac{\partial x_98}{\partial x_i\ }\ q_98+ \ \ \frac{\partial x_99}{\partial x_i\ }\ q_99\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95+ \ \frac{\partial x^{\prime i}}{\partial x^96\ }\ q^96+ \ \frac{\partial x^{\prime i}}{\partial x^97\ }\ q^97+ \ \frac{\partial x^{\prime i}}{\partial x^98\ }\ q^98+ \ \frac{\partial x^{\prime i}}{\partial x^99\ }\ q^99\]
\[\ \ \frac{\partial x_1}{\partial x_i\ }\ q_1+ \ \ \frac{\partial x_2}{\partial x_i\ }\ q_2+ \ \ \frac{\partial x_3}{\partial x_i\ }\ q_3+ \ \ \frac{\partial x_4}{\partial x_i\ }\ q_4+ \ \ \frac{\partial x_5}{\partial x_i\ }\ q_5+ \ \ \frac{\partial x_6}{\partial x_i\ }\ q_6+ \ \ \frac{\partial x_7}{\partial x_i\ }\ q_7+ \ \ \frac{\partial x_8}{\partial x_i\ }\ q_8+ \ \ \frac{\partial x_9}{\partial x_i\ }\ q_9+ \ \ \frac{\partial x_10}{\partial x_i\ }\ q_10+ \ \ \frac{\partial x_11}{\partial x_i\ }\ q_11+ \ \ \frac{\partial x_12}{\partial x_i\ }\ q_12+ \ \ \frac{\partial x_13}{\partial x_i\ }\ q_13+ \ \ \frac{\partial x_14}{\partial x_i\ }\ q_14+ \ \ \frac{\partial x_15}{\partial x_i\ }\ q_15+ \ \ \frac{\partial x_16}{\partial x_i\ }\ q_16+ \ \ \frac{\partial x_17}{\partial x_i\ }\ q_17+ \ \ \frac{\partial x_18}{\partial x_i\ }\ q_18+ \ \ \frac{\partial x_19}{\partial x_i\ }\ q_19+ \ \ \frac{\partial x_20}{\partial x_i\ }\ q_20+ \ \ \frac{\partial x_21}{\partial x_i\ }\ q_21+ \ \ \frac{\partial x_22}{\partial x_i\ }\ q_22+ \ \ \frac{\partial x_23}{\partial x_i\ }\ q_23+ \ \ \frac{\partial x_24}{\partial x_i\ }\ q_24+ \ \ \frac{\partial x_25}{\partial x_i\ }\ q_25+ \ \ \frac{\partial x_26}{\partial x_i\ }\ q_26+ \ \ \frac{\partial x_27}{\partial x_i\ }\ q_27+ \ \ \frac{\partial x_28}{\partial x_i\ }\ q_28+ \ \ \frac{\partial x_29}{\partial x_i\ }\ q_29+ \ \ \frac{\partial x_30}{\partial x_i\ }\ q_30+ \ \ \frac{\partial x_31}{\partial x_i\ }\ q_31+ \ \ \frac{\partial x_32}{\partial x_i\ }\ q_32+ \ \ \frac{\partial x_33}{\partial x_i\ }\ q_33+ \ \ \frac{\partial x_34}{\partial x_i\ }\ q_34+ \ \ \frac{\partial x_35}{\partial x_i\ }\ q_35+ \ \ \frac{\partial x_36}{\partial x_i\ }\ q_36+ \ \ \frac{\partial x_37}{\partial x_i\ }\ q_37+ \ \ \frac{\partial x_38}{\partial x_i\ }\ q_38+ \ \ \frac{\partial x_39}{\partial x_i\ }\ q_39+ \ \ \frac{\partial x_40}{\partial x_i\ }\ q_40+ \ \ \frac{\partial x_41}{\partial x_i\ }\ q_41+ \ \ \frac{\partial x_42}{\partial x_i\ }\ q_42+ \ \ \frac{\partial x_43}{\partial x_i\ }\ q_43+ \ \ \frac{\partial x_44}{\partial x_i\ }\ q_44+ \ \ \frac{\partial x_45}{\partial x_i\ }\ q_45+ \ \ \frac{\partial x_46}{\partial x_i\ }\ q_46+ \ \ \frac{\partial x_47}{\partial x_i\ }\ q_47+ \ \ \frac{\partial x_48}{\partial x_i\ }\ q_48+ \ \ \frac{\partial x_49}{\partial x_i\ }\ q_49+ \ \ \frac{\partial x_50}{\partial x_i\ }\ q_50+ \ \ \frac{\partial x_51}{\partial x_i\ }\ q_51+ \ \ \frac{\partial x_52}{\partial x_i\ }\ q_52+ \ \ \frac{\partial x_53}{\partial x_i\ }\ q_53+ \ \ \frac{\partial x_54}{\partial x_i\ }\ q_54+ \ \ \frac{\partial x_55}{\partial x_i\ }\ q_55+ \ \ \frac{\partial x_56}{\partial x_i\ }\ q_56+ \ \ \frac{\partial x_57}{\partial x_i\ }\ q_57+ \ \ \frac{\partial x_58}{\partial x_i\ }\ q_58+ \ \ \frac{\partial x_59}{\partial x_i\ }\ q_59+ \ \ \frac{\partial x_60}{\partial x_i\ }\ q_60+ \ \ \frac{\partial x_61}{\partial x_i\ }\ q_61+ \ \ \frac{\partial x_62}{\partial x_i\ }\ q_62+ \ \ \frac{\partial x_63}{\partial x_i\ }\ q_63+ \ \ \frac{\partial x_64}{\partial x_i\ }\ q_64+ \ \ \frac{\partial x_65}{\partial x_i\ }\ q_65+ \ \ \frac{\partial x_66}{\partial x_i\ }\ q_66+ \ \ \frac{\partial x_67}{\partial x_i\ }\ q_67+ \ \ \frac{\partial x_68}{\partial x_i\ }\ q_68+ \ \ \frac{\partial x_69}{\partial x_i\ }\ q_69+ \ \ \frac{\partial x_70}{\partial x_i\ }\ q_70+ \ \ \frac{\partial x_71}{\partial x_i\ }\ q_71+ \ \ \frac{\partial x_72}{\partial x_i\ }\ q_72+ \ \ \frac{\partial x_73}{\partial x_i\ }\ q_73+ \ \ \frac{\partial x_74}{\partial x_i\ }\ q_74+ \ \ \frac{\partial x_75}{\partial x_i\ }\ q_75+ \ \ \frac{\partial x_76}{\partial x_i\ }\ q_76+ \ \ \frac{\partial x_77}{\partial x_i\ }\ q_77+ \ \ \frac{\partial x_78}{\partial x_i\ }\ q_78+ \ \ \frac{\partial x_79}{\partial x_i\ }\ q_79+ \ \ \frac{\partial x_80}{\partial x_i\ }\ q_80+ \ \ \frac{\partial x_81}{\partial x_i\ }\ q_81+ \ \ \frac{\partial x_82}{\partial x_i\ }\ q_82+ \ \ \frac{\partial x_83}{\partial x_i\ }\ q_83+ \ \ \frac{\partial x_84}{\partial x_i\ }\ q_84+ \ \ \frac{\partial x_85}{\partial x_i\ }\ q_85+ \ \ \frac{\partial x_86}{\partial x_i\ }\ q_86+ \ \ \frac{\partial x_87}{\partial x_i\ }\ q_87+ \ \ \frac{\partial x_88}{\partial x_i\ }\ q_88+ \ \ \frac{\partial x_89}{\partial x_i\ }\ q_89+ \ \ \frac{\partial x_90}{\partial x_i\ }\ q_90+ \ \ \frac{\partial x_91}{\partial x_i\ }\ q_91+ \ \ \frac{\partial x_92}{\partial x_i\ }\ q_92+ \ \ \frac{\partial x_93}{\partial x_i\ }\ q_93+ \ \ \frac{\partial x_94}{\partial x_i\ }\ q_94+ \ \ \frac{\partial x_95}{\partial x_i\ }\ q_95+ \ \ \frac{\partial x_96}{\partial x_i\ }\ q_96+ \ \ \frac{\partial x_97}{\partial x_i\ }\ q_97+ \ \ \frac{\partial x_98}{\partial x_i\ }\ q_98+ \ \ \frac{\partial x_99}{\partial x_i\ }\ q_99+ \ \ \frac{\partial x_100}{\partial x_i\ }\ q_100\]
~~~~~~~~~~~~~~\[\ \frac{\partial x^{\prime i}}{\partial x^1\ }\ q^1+ \ \frac{\partial x^{\prime i}}{\partial x^2\ }\ q^2+ \ \frac{\partial x^{\prime i}}{\partial x^3\ }\ q^3+ \ \frac{\partial x^{\prime i}}{\partial x^4\ }\ q^4+ \ \frac{\partial x^{\prime i}}{\partial x^5\ }\ q^5+ \ \frac{\partial x^{\prime i}}{\partial x^6\ }\ q^6+ \ \frac{\partial x^{\prime i}}{\partial x^7\ }\ q^7+ \ \frac{\partial x^{\prime i}}{\partial x^8\ }\ q^8+ \ \frac{\partial x^{\prime i}}{\partial x^9\ }\ q^9+ \ \frac{\partial x^{\prime i}}{\partial x^10\ }\ q^10+ \ \frac{\partial x^{\prime i}}{\partial x^11\ }\ q^11+ \ \frac{\partial x^{\prime i}}{\partial x^12\ }\ q^12+ \ \frac{\partial x^{\prime i}}{\partial x^13\ }\ q^13+ \ \frac{\partial x^{\prime i}}{\partial x^14\ }\ q^14+ \ \frac{\partial x^{\prime i}}{\partial x^15\ }\ q^15+ \ \frac{\partial x^{\prime i}}{\partial x^16\ }\ q^16+ \ \frac{\partial x^{\prime i}}{\partial x^17\ }\ q^17+ \ \frac{\partial x^{\prime i}}{\partial x^18\ }\ q^18+ \ \frac{\partial x^{\prime i}}{\partial x^19\ }\ q^19+ \ \frac{\partial x^{\prime i}}{\partial x^20\ }\ q^20+ \ \frac{\partial x^{\prime i}}{\partial x^21\ }\ q^21+ \ \frac{\partial x^{\prime i}}{\partial x^22\ }\ q^22+ \ \frac{\partial x^{\prime i}}{\partial x^23\ }\ q^23+ \ \frac{\partial x^{\prime i}}{\partial x^24\ }\ q^24+ \ \frac{\partial x^{\prime i}}{\partial x^25\ }\ q^25+ \ \frac{\partial x^{\prime i}}{\partial x^26\ }\ q^26+ \ \frac{\partial x^{\prime i}}{\partial x^27\ }\ q^27+ \ \frac{\partial x^{\prime i}}{\partial x^28\ }\ q^28+ \ \frac{\partial x^{\prime i}}{\partial x^29\ }\ q^29+ \ \frac{\partial x^{\prime i}}{\partial x^30\ }\ q^30+ \ \frac{\partial x^{\prime i}}{\partial x^31\ }\ q^31+ \ \frac{\partial x^{\prime i}}{\partial x^32\ }\ q^32+ \ \frac{\partial x^{\prime i}}{\partial x^33\ }\ q^33+ \ \frac{\partial x^{\prime i}}{\partial x^34\ }\ q^34+ \ \frac{\partial x^{\prime i}}{\partial x^35\ }\ q^35+ \ \frac{\partial x^{\prime i}}{\partial x^36\ }\ q^36+ \ \frac{\partial x^{\prime i}}{\partial x^37\ }\ q^37+ \ \frac{\partial x^{\prime i}}{\partial x^38\ }\ q^38+ \ \frac{\partial x^{\prime i}}{\partial x^39\ }\ q^39+ \ \frac{\partial x^{\prime i}}{\partial x^40\ }\ q^40+ \ \frac{\partial x^{\prime i}}{\partial x^41\ }\ q^41+ \ \frac{\partial x^{\prime i}}{\partial x^42\ }\ q^42+ \ \frac{\partial x^{\prime i}}{\partial x^43\ }\ q^43+ \ \frac{\partial x^{\prime i}}{\partial x^44\ }\ q^44+ \ \frac{\partial x^{\prime i}}{\partial x^45\ }\ q^45+ \ \frac{\partial x^{\prime i}}{\partial x^46\ }\ q^46+ \ \frac{\partial x^{\prime i}}{\partial x^47\ }\ q^47+ \ \frac{\partial x^{\prime i}}{\partial x^48\ }\ q^48+ \ \frac{\partial x^{\prime i}}{\partial x^49\ }\ q^49+ \ \frac{\partial x^{\prime i}}{\partial x^50\ }\ q^50+ \ \frac{\partial x^{\prime i}}{\partial x^51\ }\ q^51+ \ \frac{\partial x^{\prime i}}{\partial x^52\ }\ q^52+ \ \frac{\partial x^{\prime i}}{\partial x^53\ }\ q^53+ \ \frac{\partial x^{\prime i}}{\partial x^54\ }\ q^54+ \ \frac{\partial x^{\prime i}}{\partial x^55\ }\ q^55+ \ \frac{\partial x^{\prime i}}{\partial x^56\ }\ q^56+ \ \frac{\partial x^{\prime i}}{\partial x^57\ }\ q^57+ \ \frac{\partial x^{\prime i}}{\partial x^58\ }\ q^58+ \ \frac{\partial x^{\prime i}}{\partial x^59\ }\ q^59+ \ \frac{\partial x^{\prime i}}{\partial x^60\ }\ q^60+ \ \frac{\partial x^{\prime i}}{\partial x^61\ }\ q^61+ \ \frac{\partial x^{\prime i}}{\partial x^62\ }\ q^62+ \ \frac{\partial x^{\prime i}}{\partial x^63\ }\ q^63+ \ \frac{\partial x^{\prime i}}{\partial x^64\ }\ q^64+ \ \frac{\partial x^{\prime i}}{\partial x^65\ }\ q^65+ \ \frac{\partial x^{\prime i}}{\partial x^66\ }\ q^66+ \ \frac{\partial x^{\prime i}}{\partial x^67\ }\ q^67+ \ \frac{\partial x^{\prime i}}{\partial x^68\ }\ q^68+ \ \frac{\partial x^{\prime i}}{\partial x^69\ }\ q^69+ \ \frac{\partial x^{\prime i}}{\partial x^70\ }\ q^70+ \ \frac{\partial x^{\prime i}}{\partial x^71\ }\ q^71+ \ \frac{\partial x^{\prime i}}{\partial x^72\ }\ q^72+ \ \frac{\partial x^{\prime i}}{\partial x^73\ }\ q^73+ \ \frac{\partial x^{\prime i}}{\partial x^74\ }\ q^74+ \ \frac{\partial x^{\prime i}}{\partial x^75\ }\ q^75+ \ \frac{\partial x^{\prime i}}{\partial x^76\ }\ q^76+ \ \frac{\partial x^{\prime i}}{\partial x^77\ }\ q^77+ \ \frac{\partial x^{\prime i}}{\partial x^78\ }\ q^78+ \ \frac{\partial x^{\prime i}}{\partial x^79\ }\ q^79+ \ \frac{\partial x^{\prime i}}{\partial x^80\ }\ q^80+ \ \frac{\partial x^{\prime i}}{\partial x^81\ }\ q^81+ \ \frac{\partial x^{\prime i}}{\partial x^82\ }\ q^82+ \ \frac{\partial x^{\prime i}}{\partial x^83\ }\ q^83+ \ \frac{\partial x^{\prime i}}{\partial x^84\ }\ q^84+ \ \frac{\partial x^{\prime i}}{\partial x^85\ }\ q^85+ \ \frac{\partial x^{\prime i}}{\partial x^86\ }\ q^86+ \ \frac{\partial x^{\prime i}}{\partial x^87\ }\ q^87+ \ \frac{\partial x^{\prime i}}{\partial x^88\ }\ q^88+ \ \frac{\partial x^{\prime i}}{\partial x^89\ }\ q^89+ \ \frac{\partial x^{\prime i}}{\partial x^90\ }\ q^90+ \ \frac{\partial x^{\prime i}}{\partial x^91\ }\ q^91+ \ \frac{\partial x^{\prime i}}{\partial x^92\ }\ q^92+ \ \frac{\partial x^{\prime i}}{\partial x^93\ }\ q^93+ \ \frac{\partial x^{\prime i}}{\partial x^94\ }\ q^94+ \ \frac{\partial x^{\prime i}}{\partial x^95\ }\ q^95+ \ \frac{\partial x^{\prime i}}{\partial x^96\ }\ q^96+ \ \frac{\partial x^{\prime i}}{\partial x^97\ }\ q^97+ \ \frac{\partial x^{\prime i}}{\partial x^98\ }\ q^98+ \ \frac{\partial x^{\prime i}}{\partial x^99\ }\ q^99+ \ \frac{\partial x^{\prime i}}{\partial x^100\ }\ q^100\]