#### Answer

The solution is
$$\frac{\partial}{\partial u}g(u,v)=10uv(u^2v-v^3)^4;$$
$$\frac{\partial}{\partial v}g(u,v)=5(u^2v-v^3)^4(u^2-3v^2)$$

#### Work Step by Step

Regard $v$ and as a constant and differentiate with respect to $u$:
$$\frac{\partial}{\partial u}g(u,v)=\frac{\partial}{\partial u}\bigg((u^2v-v^3)^5\bigg)=5(u^2v-v^3)^4(u^2v-v^3)^{'}_u=5(u^2v-v^3)^4\cdot2uv=10uv(u^2v-v^3)^4.$$
Regard $u$ as constand and differentiate with respect to $v$:
$$\frac{\partial}{\partial v}g(u,v)=\frac{\partial}{\partial v}\bigg((u^2v-v^3)^5\bigg)=5(u^2v-v^3)^4(u^2v-v^3)^{'}_u=5(u^2v-v^3)^4(u^2-3v^2).$$