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Can anyone help me proofing this? This is not homework.

  1. Sep 23, 2010 #1
    This is part of a bigger derivation of Green's function. The book just jump to the ending and I cannot understand how to do this. I need someone to give me guidence how to proof this:

    [tex] \frac{x}{r} \frac{\partial u}{\partial x} + \frac{y}{r} \frac{\partial u}{\partial y} +\frac{z}{r} \frac{\partial u}{\partial z} \;=\; \frac{\partial u}{\partial r} [/tex]


    [tex] r=\sqrt{x^2+y^2+z^2}[/tex]

    This is not a homework problem.

  2. jcsd
  3. Sep 23, 2010 #2


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    Use the chain rule:

    [tex]\frac{\partial u}{\partial r}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial r}+\cdots[/tex]
  4. Sep 23, 2010 #3
    I thought of that, but what is [tex]\frac{\partial x}{\partial r}[/tex]

    I know

    [tex]\frac{\partial r}{\partial x}=\frac{x}{r}[/tex]

    That's exactly where I got stuck!!!
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