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Math Help - Quick question

  1. #1
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    Quick question

    if I have u = ln(root(x^2 + y^2)) then in the first partial derivative d^2u/dx^2 (or Uxx in other words) should I get 2x/root(x^2 + y^2) or -x/(x^2 + y^2)^3/2.

    I need to remember what I have to do exactly and I won't ask too many questions like this as I would be spamming the boards.

    Please reply soon, thanks.
    Last edited by Undefdisfigure; October 19th 2007 at 02:21 PM.
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  2. #2
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    u = \ln \left( {\sqrt {x^2  + y^2 } } \right) = \frac{{\ln \left( {x^2  + y^2 } \right)}}{2}

    u_x  = \frac{x}{{x^2  + y^2 }}\quad \quad u_{xx}  = \frac{{y^2  - x^2 }}{{\left( {x^2  + y^2 } \right)^2 }}<br />
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  3. #3
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    Looks like I was wrong entirely. But how did you derive u= ln(root(x^2 + y^2)) = ln(x^2 + y^2)/2 Plato, or anybody else if they know...
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  4. #4
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    x > 0\quad  \Rightarrow \quad \ln \left( {\sqrt x } \right) = \ln \left( {x^{\frac{1}{2}} } \right) = \left( {\frac{1}{2}} \right)\ln (x)<br /> <br />
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