If $w = f ( x , y , z )$

Short Answer

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