Chain Rule Application: Solving a First Year Uni Math Problem

[3pear]

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!

 

[waht]

do you know the chain rule?

 

[3pear]

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

 

[Random Variable]

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

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

 

[3pear]

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...

 

[Random Variable]

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

 

[3pear]

oh!i got it~~~ thanks mates~