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Math Help - Logarithmic Differentiation

  1. #1
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    Logarithmic Differentiation

    How would i differentiate this

    <br />
ln(lnx^2)<br />

    im trying to do it right now but im getting alot
    of fractions

    i think i got it does it look something like this

    (1/lnx^2) (2/x)
    Last edited by john doe; October 13th 2008 at 12:47 AM.
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  2. #2
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    Your answer is correct.

    You could have made life a bit easier for yourself by using properties of logarithms. In fact, \ln(x^2)=2\ln x, so \ln(\ln(x^2)) = \ln(2\ln x) = \ln2 + \ln(\ln x). Then when you differentiate, the first term is constant, so it disappears and you only have to deal with the second term.
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  3. #3
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    answer

    Isn't it 1/(xlnx) ?
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  4. #4
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    Quote Originally Posted by Jasonium View Post
    Isn't it 1/(xlnx) ?
    No, it's \frac{1}{x \ln|x|} which is a simplified form of the answer found by the OP.
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  5. #5
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    Quote Originally Posted by Opalg View Post
    Your answer is correct.

    You could have made life a bit easier for yourself by using properties of logarithms. In fact, \ln(x^2)=2\ln x, so \ln(\ln(x^2)) = \ln(2\ln x) = \ln2 + \ln(\ln x). Then when you differentiate, the first term is constant, so it disappears and you only have to deal with the second term.
    I think it might be \ln(\ln(x^2)) = \ln(2\ln x) = \ln2 + \ln(\ln {\color{red}|}x{\color{red}|}) .....
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