# Define z as a function of x and y

## 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 $$\frac{\partial u}{\partial x}$$

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.

## Answers and Replies

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Did you mean to say you're trying to find $\partial u/\partial x$ and not $\partial z/\partial x$?

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

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Frankly, I don't see why z has anything to do with the problem then.