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Math Help - Partial Derivative at the origin.

  1. #1
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    Partial Derivative at the origin.

    Let f(x, y) = sqrt( abs(xy))

    Verify that the x partial derivative and the y partial derivative are both 0 at the origin.

    Once I take the partial derivative, I can't substitute (0, 0) because then I would get 0/0. How do I go around this problem?
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  2. #2
    MHF Contributor chisigma's Avatar
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    The only You have to do is to apply the definitions...

    \displaystyle \frac{\partial f(x,y)}{\partial x}= \lim_{h \rightarrow 0} \frac{f(x+h,y) - f(x,y)}{h}

    \displaystyle \frac{\partial f(x,y)}{\partial y}= \lim_{h \rightarrow 0} \frac{f(x,y+h) - f(x,y)}{h}

    ... for f(x,y)= \sqrt{|x\ y|} ...

    Kind regards

    \chi \sigma
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