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Math Help - logarithmic differentiation

  1. #1
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    logarithmic differentiation

    How does one use logarithmic differentiation to differentiate this function:

    f(x) = x^x
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Quixotic View Post
    How does one use logarithmic differentiation to differentiate this function:

    f(x) = x^x
    \ln\text{ }f=x\ln(x) so that \frac{f'}{f}=1+\ln(x) and so f'=f\left(1+\ln(x)\right), but f=x^x and so f'=x^x\left(1+\ln(x)\right)
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    MHF Contributor Drexel28's Avatar
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    Quixotic, huh? Like hopelessly capricious?
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  4. #4
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    Quote Originally Posted by Drexel28 View Post
    Quixotic, huh? Like hopelessly capricious?
    Yes. Sudden, unreachable goals are a hobby of mine.
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