# Homework Help: Partial Derivative

1. Dec 17, 2007

### jesuslovesu

Whoops got it now, didn't carry out my substitutions far enough.

1. The problem statement, all variables and given/known data
$$z = x^2 + 2y^2$$
$$x = rcos(\theta)$$
$$y = rsin(\theta)$$
2. Relevant equations

3. The attempt at a solution
Find $$(\partial z/\partial x)$$ (theta is constant)

dz = 2xdx + 4ydy
dx = cos$$(\theta)$$dr - rsin$$(\theta)$$d$$\theta$$
dy = sin$$(\theta)$$dr + rcos$$(\theta)$$d$$\theta$$

Unfortunately I'm not really quite sure where to go from here, I know that
$$(\frac{ \partial z } { \partial x} )$$ is 2x when y is constant. But how to factor in theta being constant?
I suppose I could reduce
dx to dx = cos$$(\theta)$$dr
and dy = sin$$(\theta)$$dr

Last edited: Dec 17, 2007
2. Dec 17, 2007

### HallsofIvy

If $\theta$ is a constant, then $d\theta= 0$

Yes, that is exactly correct. Then dz= dx+ dy= ?