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Math Help - Derivatives of Logarithmic and Exponential Function

  1. #1
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    Derivatives of Logarithmic and Exponential Function

    y = (1+ log(x-numerator)3-base) / x

    I didnt know how to write the log but the numerator is x and the base is 3.

    Thanks in advance
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  2. #2
    Jen
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    Quote Originally Posted by rhhs11 View Post
    y = (1+ log(x-numerator)3-base) / x

    I didnt know how to write the log but the numerator is x and the base is 3.

    Thanks in advance
    Before I try anything, let me make sure I have read your explanation right...

    f(x)=\frac{1+\log_3{x}}{x}

    Is this what you meant?
    Last edited by Jen; March 27th 2008 at 09:16 PM.
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  3. #3
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    Everything is over including 1. So its (1+log..) / x

    Thanks
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  4. #4
    Jen
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    <br />
f(x)=\frac{1+\log_3{x}}{x}<br />

    First lets use the change of base property to get rid of the \log_3{x}

    \log_3{x}=\frac{\ln{x}}{\ln{3}}

    Substituting this we get,

    f(x)=\frac{1+\frac{\ln{x}}{\ln{3}}}{x}

    Now to diferentiate this you need to either bring up the x and use the product rule or use the quotient rule.

    \frac{d}{dx}f(x)=\left(1+ \frac{1}{\ln{3}}\ln{x}\right)(-x^{-2})+(x^{-1})\left( \frac{1}{\ln{x}}\left(\frac{1}{x}\right)\right)

    Doing several steps of simplification and using a sum of logarithms property we get...

    \frac{d}{dx}f(x)=\frac{\ln{3x}-1}{x^2\ln{3}}
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