Use the chain rule to find z(s) and z(t) if f(x,y)=x^2y+2xy^3
So you want to find and given:
Since z depends on both x and y,
(treating t as a constant). It's just the chain rule for two variables, except z depends on variables other than s, so you're looking for a partial derivative.
The situation for is similar.
That should get you going in the right direction. Post again if you have any more trouble.