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Thread: Logarithmic Differentation

  1. #1
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    Logarithmic Differentation

    Any help with solving this... I can't figure it out.

    $\displaystyle 3^xlog_8(x)$

    That is, I need to find the derivative. I think this is the first step:

    $\displaystyle ln(3)/ln(8) $
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  2. #2
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    $\displaystyle 3^x \log_8 x = \frac{3^x \ln x}{\ln 8}$
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  3. #3
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    Do i continue with using the quetient rule. Is f'(x)= $\displaystyle 3^xln(x)*3$?
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  4. #4
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    Quote Originally Posted by cjmac87 View Post
    Do i continue with using the quetient rule. Is f'(x)= $\displaystyle 3^xln(x)*3$?


    $\displaystyle \frac{3^x \ln{x}}{\ln{8}} = \frac{1}{\ln{8}} \cdot 3^x \ln{x}
    $

    use the product rule ...

    $\displaystyle \frac{1}{\ln{8}}\left(3^x \cdot \frac{1}{x} + 3^x \cdot \ln{3} \cdot \ln{x}\right)$

    now clean up the algebra.
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