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Derivative problem - e^(x^x)

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Problem: e(x^x)

    3. The attempt at a solution

    I came up with - f'(x) = e(x^x)[ln(x)+1]. The solution should be - x^x*e(x^x)[ln(x)+1] . Can someone please help me understand why should I add x^x to the solution.

    Much appreciated!
     
  2. jcsd
  3. Dec 16, 2011 #2

    dextercioby

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    Science Advisor
    Homework Helper

    You should use chain rule and logarithmic differentiation. First use the chain rule.
     
  4. Dec 16, 2011 #3
    Aha, so I should just apply it like that -

    f(x) = e(x^x) -> f'(x) = e(x^x)

    g(x) = x^x -> ln(g(x))=x*ln(x) -> g'(x)=x^x(ln(x)+1)

    (f°g)'(x) = e(x^x)*x^x(ln(x)+1)

    Thank you very much!
     
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