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It's crazy, I don't see where I goes wrong. Lookit..

[tex]\frac{\partial}{\partial x} \left(\frac{x}{z\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2}\right)} \right) [/tex]

[tex]= \left(\frac{1}{z\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2}\right)} \right)[/tex]

[tex]+(x/z)(-1)\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2}\right)^{-2}\left((1/2)(x^2+y^2)^{-1/2}2x+(1/z^2)(3/2)\sqrt{x^2+y^2}2x\right)[/tex]

[tex]= \left(\frac{1}{z\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2}\right)} \right) [/tex]

[tex]-\frac{3x^2\sqrt{x^2+y^2}}{z^3\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2}\right)^2}[/tex]

[tex]-\frac{x^2}{z\sqrt{x^2+y^2}\left(\sqrt{x^2+y^2} +\frac{\sqrt{x^2+y^2}^3}{z^2} \right)^2}[/tex]

The first term agrees with Mapple but not the second and third.

In the second, the 3 is a 2 and in the third, the big parenthesis is not raised to the 2. (it's to the 1)

I have checked using the command 'simplify' that our two expressions are not equivalent. what Mapple does is that it get a (x²+y²)^½ out of the parenthesis before taking the derivative. And the worst thing is, when I do that too, I get the same result as mapple, but not when I don't take out (x²+y²)^½ first. I've banged my head on the desk for hours on this and get's see why I don't get the same answer by the two "methods". Help me obi-wan kenobi. You are my only hope.

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# Help me get this derivative right!

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