Partial derivatives/ total derivative

[zell99]

Homework Statement

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,

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

 

[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= e^xcos(y), v= e^xsin(y) and F(u,v)= f(x,y).

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

 

[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.

 

[zell99]

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

 

[zell99]

Solved it.