Define z as a function of x and y

[MeMoses]

Homework Statement

The equations x=uv, y=u+v and z=u^2-v^2 define z as a function of x and y. Find $$\frac{\partial u}{\partial x}$$

Homework Equations

Chain rule

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.

 

[vela]

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

 

[MeMoses]

No, I meant what I stated. I realized 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

 

[vela]

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