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Math Help - Help with finding the derivative of a logarithmic function

  1. #1
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    Help with finding the derivative of a logarithmic function

    Hey, I need help with the following problem:

    Differentiate the function:
    g(x)=ln(x*(x^2 - 1)^1/2)

    Thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by luckeyduck View Post
    Hey, I need help with the following problem:

    Differentiate the function:
    g(x)=ln(x*(x^2 - 1)^1/2)

    Thanks!
    now this is doable by the chain rule. but it is easier to simplify first

    note that \ln \left[ x (x^2 - 1)^{1/2} \right] = \ln \left[ x (x + 1)^{1/2} (x - 1)^{1/2} \right] = \ln x + \frac 12 \ln (x + 1) + \frac 12 \ln (x - 1)

    now you can differentiate each of those terms, right?
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