If $$z = \sin\!\left(x^{2}+y^{2}\right),\qquad x = v\cos\!\left(u\right),\qquad y = v\sin\!\left(u\right),$$ find $\partial z/\partial u$ and $\partial z/\partial v$. The variables are restricted to domains on which the functions are defined.

$\partial z/\partial u =$

$\partial z/\partial v =$