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Math Help - Derivative of Natural Log Function

  1. #1
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    Exclamation Derivative of Natural Log Function

    f(x)=ln[(squareroot(x^2+1)) / (x(2x^3-1)^2)]

    Quotient Rule is where im starting off at but i can't get past that. Need help on this problem.Thanks.
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  2. #2
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    Quote Originally Posted by PMoNEY23 View Post
    f(x)=ln[(squareroot(x^2+1)) / (x(2x^3-1)^2)]

    Quotient Rule is where im starting off at but i can't get past that. Need help on this problem.Thanks.
    It would be neater if you use laws of logs and split the expression into:
    \ln{\sqrt{x^2+1}}-\ln{(x(2x^3-1)^2)} = \frac{1}{2}\ln{(x^2+1)}-\ln{(x)}-2\ln{(2x^3-1)}

    Then apply what you know of derivatives of logarithms and chain rule.
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  3. #3
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    <br />
\ln{\sqrt{x^2+1}}-\ln{(x(2x^3-1)^2)} = \frac{1}{2}\ln{(x^2+1)}-\ln{(x)}-2\ln{(2x^3-1)}<br />
    Remember that \frac{d}{dx}ln(f(x))=\frac{f'(x)}{f(x)}.

    For example (here's the first one!) \frac{d}{dx} \frac{1}{2}ln(x^2+1)=\frac{1}{2}. \frac{2x}{x^2+1}=\frac{x}{x^2+1}.

    All you need to do now is repeat this process for each of the other ones.
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