# Partial derivatives/ total derivative

by zell99
Tags: derivative, derivatives or, partial
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 P: 13 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 Attached Thumbnails
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,569 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: $$\frac{\partial f}{\partial x}= \frac{\partial F}{\partial u}\frac{\partial u}{\partial x}+ \frac{\partial F}{\partial v}\frac{\partial v}{\partial x}$$
 P: 13 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.
 P: 13 Partial derivatives/ total derivative Just to clarify since my use of 'last part' wasn't particularly precise, it's part (c) I'm struggling with. Thank you
 P: 13 Solved it.

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