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Math Help - Logarithmic differentiation

  1. #1
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    Logarithmic differentiation

    How do I solve [ln(x)]^(ln(x))?

    I arrived at e^[ln(x)ln[lx(x)] . [1/x . ln[ln(x)]+ln(x).(1/(xln(x))]
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    Re: Logarithmic differentiation

    You can't SOLVE anything as you don't have an EQUATION.

    However, if as your title suggests, you are trying to find the DERIVATIVE of \displaystyle \begin{align*} y = \left[ \ln{(x)} \right] ^{\ln{(x)}} \end{align*}, then start by taking the logarithm of both sides and simplify the RHS before differentiating.
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  3. #3
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    Re: Logarithmic differentiation

    That's what I did but the answer turned out very differently.
    Could you demonstrate to to me?

    How do I express e^[ln(x)ln(ln(x)] as a power of x?
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    Re: Logarithmic differentiation

    No, I want you to try it yourself. You need to post exactly what you tried, then we can see where you've gone wrong (if at all).
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    Re: Logarithmic differentiation

    I spent 4 hrs on this question. The reason why I don't like typing equations using keyboard is because it's slow and frustrating, especially when the equation becomes long and chaotic.
    Simply put, I utilized ln, e and the chain rule to differentiate the RHS. Answer turned out very differently, however. Using the same mathematical reasoning, I have no issues with the other question. It's probably a matter of algebraic simplification-hence, I want the confirmation.
    If that is true-a matter of simplication-then, I'll skip past the question as I never bother with the rudimentary concrete details.

    I applied chain rule to y = e^[ln(x)ln(ln(x)] and I'm very sure I have to. If you could tell me if this part is correct, it is sufficient as the steps beyond the chain rules are tautological simplication.
    Last edited by Darrylcwc; November 16th 2013 at 11:09 PM.
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    Re: Logarithmic differentiation

    Solved.
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