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F(x)=x^log(x) differentiation

  1. Jan 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of the following function f.


    2. Relevant equations

    f(x)=x^log(x)

    3. The attempt at a solution

    I really don't know how to do this, as it's x to the power of a function of x.
     
  2. jcsd
  3. Jan 16, 2009 #2

    D H

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    Re: differentiation

    Use the fact that for any function u(x),

    [tex]u(x) = e^{\ln(u(x))}[/tex]
     
  4. Jan 16, 2009 #3

    HallsofIvy

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    Re: differentiation

    Or (almost the same thing) use "logarithmic differentiation".

    If y= xlog x then log(y)= log(xlog(x))= log(x)log(x).

    Differentiate both sides with respect to x, using the chain rule on the left side, and then solve for dy/dx.
     
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