Homework Help: Partial derivatives/ total derivative

1. Dec 21, 2006

zell99

1. The problem statement, all variables and given/known data
I've attactched an image of the question, I hope this is ok, if not let me know and I'll copy it out onto a post,

3. The attempt at a solution
I've done parts (a) and (b) using the total derivative of f ( http://mathworld.wolfram.com/TotalDerivative.html ) but I can't get started on the last part. I've tried differentiating the expressions found in (a) but it doesn't seem to lead anywhere.

A push in the right direction would be appreciated.
Thanks

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2. Dec 21, 2006

HallsofIvy

You have the definitions. All I can say is "just do it"! You are asked to show that
$$\frac{\partial f}{\partial x}= u\frac{\partial F}{\partial u}+ v\frac{\partial F}{\partial v}$$
u= excos(y), v= exsin(y) and F(u,v)= f(x,y).

You will need to use the chain rule:
$$\frac{\partial f}{\partial x}= \frac{\partial F}{\partial u}\frac{\partial u}{\partial x}+ \frac{\partial F}{\partial v}\frac{\partial v}{\partial x}$$

3. Dec 21, 2006

zell99

Thanks for the reply: I've done parts (a) and (b) already, it's the third part I'm struggling with (I can't quite see how your post relates to this bit). I won't post my solutions for these bits unless thay would be helpful, since they are show that... questions.

Last edited: Dec 21, 2006
4. Dec 21, 2006

zell99

Just to clarify since my use of 'last part' wasn't particularly precise, it's part (c) I'm struggling with.
Thank you

5. Dec 22, 2006

Solved it.