# First year uni math problem

first year uni math problem~~

if w=f(u,v)has continuous partial derivatives and u=x+y
and v=x-y,use the chain rule to show that

(dw/dx)/(dw/dy)=(df/du)^2-(df/dv)^2

this is a first year uni math problem,is there anyone can help we with it??
thx a lot!

do you know the chain rule?

yeah i know,but no idea hw do i apply on this question~~

$$\frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x}$$

$$\frac{\partial w}{\partial y} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial y} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial y}$$

ok,i got it,but i still not clear which varible i take respect to when i differenciate for u=x+y and v=x-y....

$$\frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x} = \frac{\partial f}{\partial u}*1 + \frac{\partial f}{\partial v}*1 = \frac{\partial f}{\partial u} + \frac{\partial f}{\partial v}$$

oh!!!!i got it~~~ thx mates~