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I want to show that $f(x,y)=|xy|^{1/2}$ is differentiable at $(1,1)$.

I am trying to use that formula $\frac{f(h,k)-f(a,b)-Df(a,b)(h,k)}{ \|(h,k)\|}$ to get a result. but so far I haven't figured out where I am making mistake.

in this situation $(a,b)$ is $(1,1)$ $Df$ is a total derivative.

Thank you for everyone sharing their opinion.

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The absolute value part is of absolutely no relevance near $(1,1)$. In any circle of radius $\lt 1$ about $(1,1)$, your function is simply $(x^{1/2}y^{1/2}$. There is no problem calculating partial derivatives of any order you want. –  André Nicolas Dec 11 '12 at 6:11
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