# Math Help - Partial Derivatives Question?

1. ## Partial Derivatives Question?

so, i've been having trouble with this particular problem regarding proofs and partial derivatives. i get how to evaluate them but i just can't understand this problem.

ok,so for this problem, u = f(x,y), where x = e^s cost and y = e^s sin t.
show that

(∂u/∂x)^2+(∂u/∂y)^2 = e^-2s[(∂u/∂s)^2+(∂u/∂t)^2]

The only thing you can write for $\frac{\partial u}{\partial x}$ is $\frac{\partial f}{\partial x}= f_x$ and similarly for $\frac{\partial u}{\partial y}$. For $\frac{\partial u}{\partial s}$, use the chain rule: $\frac{\partial u}{\partial s}= \frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+ \frac{\partial u}{\partial y}\frac{\partial y}{\partial s}$.