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Thread: Chain Rule

  1. #1
    Junior Member
    Aug 2009

    Chain Rule

    I am having some difficulty with a few problems which seem to be similar in a sense. One of these problems is:

    Suppose z = f(x,y) has continuous partial derivatives. Let:
    $\displaystyle x = e^r\cos\theta, y = e^r\sin\theta$ Show that then:
    $\displaystyle (\frac{\partial z}{\partial x})^2+ (\frac{\partial z}{\partial y})^2 = e^{-2r}(( \frac{\partial z}{\partial r})^2 + (\frac{\partial z}{\partial \theta})^2)$

    I am fairly lost at how to begin this. I know I could find the partial of x with respect to r or theta, but I don't know how to tie it into the question. I was absent during that class, and the book doesn't go through a problem similar to it either. Thanks for any help.
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  2. #2
    MHF Contributor Calculus26's Avatar
    Mar 2009
    See attachment
    Attached Thumbnails Attached Thumbnails Chain Rule-chainrule.jpg  
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