Use the Chain Rule to find \frac{\partial z}{\partial s} and \frac{\partial z}{\partial t}.
z = e^r \cos(\theta), \quad r = st, \quad \theta = \sqrt{s^4 + t^4}
\frac{\partial z}{\partial s} = \left( \cos(\theta) - \frac{s(\sin(\theta))}{\sqrt{s^4 + t^4}} \right) e^4
\frac{\partial z}{\partial t} =
