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Help me get this derivative right!

  1. Nov 11, 2005 #1

    quasar987

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    (And you will be greatly rewarded in the afterlife)

    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.
    :cry: :cry: :cry:
     
    Last edited: Nov 11, 2005
  2. jcsd
  3. Nov 11, 2005 #2

    VietDao29

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    It seems that this term is wrong. I get:
    [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]
    *You seem to forget a [itex]\sqrt{x ^ 2 + y ^ 2}[/itex] in the denominator...*
    You should check it again :wink:
     
  4. Nov 11, 2005 #3

    benorin

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    Here's what I got

    For that term, I get [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]

    When I simplify that term I get [tex]-\frac{x^2}{\left( x^2+y^2\right)^{\frac{3}{2}} \left( x^2+y^2+z^2\right)^2}[/tex]


    I attached a Maple worksheet with my work (I use Maple v9.51) rename the file without the .txt so it ends with .mw (PF wouldn't let me upload .mw files, but .txt OK).
     

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    Last edited: Nov 11, 2005
  5. Nov 11, 2005 #4

    quasar987

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    VietDao: you'Re right, but it was just a Latex error. I have that too and haver edited the original post.

    I still don't see where my mistake is.
    Here's what my mapple has to say:
     

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