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Differentiability of absolute value

  1. Nov 14, 2012 #1
    f: R2 to R1 given by f(x,y) = x(|y|^(1/2))
    show differentiable at (0,0)

    so I'm using the definition lim |h| ->0 (f((0,0) + 9(h1,h2)) - f(0,0) - Df(0,0) (h1,h2)) / |h|

    so first for the jacobian for f, when I'm doing the partial with respect to y, do I have to break this into the case y>0 and y<0 and show its differentiable in both cases (and maybe also have to do the same for when h2 >0 or <0) or can I use do it in one step by rewriting and by differentiating (y^2)^1/4 and. I did that and the Df(0,0) just goes away and then limit doesnt go to 0 it seems. Any help is appreciated thanks!
     
  2. jcsd
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