If $z = f ( x , y )$ Has Continuous Partial Derivatives

Essay

If $z = f ( x , y )$ has continuous partial derivatives, $x = s + 2 t$ , and $y = s - 2 t$ , show that $\frac { \delta \mathcal { d } } { \delta s} \frac { \delta z } { \delta t } = 2 \left( \frac { \delta z } { \delta x } \right) ^ { 2 } - 2 \left( \frac { \delta z } { \delta y } \right) ^ { 2 }$