Suppose $z = x^{2} \sin y$, $x = -3s^2 + t^2$, $y = -6st$.

A. Use the chain rule to find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ as functions of x, y, s and t.
$\frac{\partial z}{\partial s} =$
$\frac{\partial z}{\partial t} =$

B. Find the numerical values of $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ when $\left( s , t \right) = \left( 3 , 5 \right)$.
$\frac{\partial z}{\partial s} \left( 3 , 5 \right) =$
$\frac{\partial z}{\partial t} \left( 3 , 5 \right) =$