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Math Help - how to evaluate divergence of a function

  1. #1
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    Unhappy how to evaluate divergence of a function

    how to evaluate divergence of a function-picture_12.png
    Last edited by mr fantastic; November 23rd 2011 at 11:56 AM. Reason: Re-titled.
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  2. #2
    MHF Contributor

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    Re: how to evaluate this simple partial differential equation.

    First, this isn't a "differential equation" nor are you asked to "evaluate" anything. You are asked to find gradient of the function f(x,y,z)= \frac{1}{x^2+ y^2+ z^2}= (x^2+ y^2+ z^2)^{-1}

    The derivatives are fairly straight forward. By the chain rule,
    \frac{\partial f}{\partial x}= -1(x^2+ y^2+ z^2)^{-2}\frac{\partial (x^2+ y^2+ z^2)}{\partial x}= \frac{-2x}{(x^2+ y^2+ z^2)^2}

    Can you do the other two partial derivatives?
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