Let $w = x ^ { 3 } + y ^ { 3 } + z ^ { 3 }$

Short Answer

Let $w = x ^ { 3 } + y ^ { 3 } + z ^ { 3 }$ , $x = s + t$ , $y = s ^ { 2 } - t ^ { 2 }$ and $z = s t$ . Use the chain rule to show that $s \left( \frac { \delta w } { \delta s } \right) + t \left( \frac { \delta w } { \delta t } \right) = 3 x ^ { 3 } + 6 y ^ { 3 } + 6 z ^ { 3 }$ .