Suppose \(z = x^{2} \sin y\text{,}\) \(x = 3 s^{2} + 2 t^{2}\text{,}\) \(y = -2 s t\text{.}\)
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 \(\left( s , t \right) = \left( -3 , 3
\right)\text{.}\)
\(\frac{\partial z}{\partial s} \left( -3 , 3 \right) =\)
\(\frac{\partial z}{\partial t} \left( -3 , 3 \right) =\)