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Partial derivatives/ total derivative

by zell99
Tags: derivative, derivatives or, partial
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zell99
#1
Dec21-06, 10:53 AM
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
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HallsofIvy
#2
Dec21-06, 11:04 AM
Math
Emeritus
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Thanks
PF Gold
P: 39,510
You have the definitions. All I can say is "just do it"! You are asked to show that
[tex]\frac{\partial f}{\partial x}= u\frac{\partial F}{\partial u}+ v\frac{\partial F}{\partial v}[/tex]
u= excos(y), v= exsin(y) and F(u,v)= f(x,y).

You will need to use the chain rule:
[tex]\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}[/tex]
zell99
#3
Dec21-06, 11:13 AM
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.

zell99
#4
Dec21-06, 06:26 PM
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
zell99
#5
Dec22-06, 08:31 AM
P: 13
Solved it.


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