Partial derivatives/ total derivative

  1. 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 Files:

  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,547
    Staff Emeritus
    Science Advisor

    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]
     
  4. 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
  5. Just to clarify since my use of 'last part' wasn't particularly precise, it's part (c) I'm struggling with.
    Thank you
     
  6. Solved it.
     
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