(4 points) Suppose $z = x^2 \sin y$, $x = 3s^2 + 3t^2$, $y = 6st$.
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.
$\frac{\partial z}{\partial s} = 12sxsiny + 6x^2tcosy$
$\frac{\partial z}{\partial t} = 12xtsiny + 6x^2scosy$
B. Find the numerical values of $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ when $(s, t) = (-2, -2)$.
$\frac{\partial z}{\partial s}(-2, -2) = $
$\frac{\partial z}{\partial t}(-2, -2) = $
