# Define z as a function of x and y

1. Nov 27, 2011

### MeMoses

1. The problem statement, all variables and given/known data
The equations x=uv, y=u+v and z=u^2-v^2 define z as a function of x and y. Find $$\frac{\partial u}{\partial x}$$

2. Relevant equations

Chain rule

3. The attempt at a solution
Once I get z as a function of x and y the solution seems pretty straight forward, but how exactly is that done. Would it be along the lines of z(x(u,v),y(u,v))? That doesn't seem right though. Thanks for any help in advance.

2. Nov 27, 2011

### vela

Staff Emeritus
Did you mean to say you're trying to find $\partial u/\partial x$ and not $\partial z/\partial x$?

3. Nov 27, 2011

### MeMoses

No, I meant what I stated. I realised you solve for u and v and then plug into z=u^2-v^2. You get u=x/v and substitute that into y=u+v and then multiply both sides by v to get a quadratic equation. You do that for both u and v and plug them into z and its smooth sailing from there

4. Nov 27, 2011

### vela

Staff Emeritus
Frankly, I don't see why z has anything to do with the problem then.