Let $z = x ^ { 2 } y + x y ^ { 2 }$

Essay

Let $z = x ^ { 2 } y + x y ^ { 2 }$ and $x = 2 u + v$ , and $y = u - 3 v$ . Show that $\frac { \delta ^ { 2 } z } { \delta u \delta v } = - 16 x - 6 y$ .