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Partial Derivative of atan(xy/(1+x^2+y^2)^0.5)

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that if ##z=\arctan(\frac{xy}{\sqrt(1+x^2+y^2)})## , then:

    ##\frac{\partial^2 z}{\partial x \partial y}=\frac{1}{(1+x^2+y^2)^\frac{3}{2}} ##

    2. Relevant equations

    ##\frac{d}{d x} (\arctan(x)) = \frac{1}{1+x^2}##

    3. The attempt at a solution

    Differentiating z partially w.r.t y, I got:

    ## \frac{\partial z}{\partial y} = \frac{x^3+x}{(1+x^2+y^2)^\frac{3}{2} (1+x^2+y^2+x^2y^2)} ##

    I'm pretty sure my working till here is correct. But differentiating again w.r.t x would be disastrous. Help me please. :)
     
  2. jcsd
  3. Nov 24, 2012 #2

    tiny-tim

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    Hi MrWarlock616! :smile:

    You can cancel a (1 + x2), top-and-bottom :wink:
     
  4. Nov 24, 2012 #3
    EDIT: -nvm got it-
     
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