Prove the equality : Multivariable chain rule problem

[michonamona]

Homework Statement

Prove that

(\frac{\partial u}{\partial x})^{2} + (\frac{\partial u}{\partial t})^{2} = e^{-2s}[(\frac{\partial u}{\partial s})^{2} + (\frac{\partial u}{\partial t})^{2}].

Homework Equations

u = f(x,y)
x = e^{s}cost
y = e^{s}sint

The Attempt at a Solution

I started out by computing \frac{\partial u}{\partial s}, then solving it for \frac{\partial u}{\partial x}. Then I did the same for \frac{\partial u}{\partial y}. So I got some messy equations, that made think that there must be a much easier way to solve this. I also tried implicit differentiation but got stuck. Any insight?

Thanks,
M

 

[Mark44]

Start by evaluating the right side, and don't try to solve for u_x or u_y. If you calculate the two partials on the right side correctly, many terms will drop out.

 

[michonamona]

Ah...thank you.