(20 points) Let $f(x, y) = e^{xy^2} + 4x^2y$.
(a) (8 points) Compute $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$.
(b) (4 points) Compute $\frac{\partial^2 f}{\partial x \partial y}$.
(c) (8 points) Let $x = s + t$ and $y = s^2t$, and use the Chain Rule to compute $\frac{\partial f}{\partial s}$ and $\frac{\partial f}{\partial t}$ (You may leave your answers in terms of $x, y, s,$ and $t$).