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Math Help - Derivative of a log function to base e^x

  1. #1
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    Derivative of a log function to base e^x

    Unsure if what I am doing with this function is correct;
    I need to differentiate the following function,

    f(x) = \log_{e^x}(\sin x)
    I have used the change of base property
    \log_{b}x = \frac{\log_{a}x}{\log_{a}b}
    Thereofre;
    f(x)=\frac {\ln(\sin x)} {\ln e^x} = \frac {\ln(\sin x)} {x}
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  2. #2
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    Quote Originally Posted by Robb View Post
    Unsure if what I am doing with this function is correct;
    I need to differentiate the following function,

    f(x) = \log_{e^x}(\sin x)
    I have used the change of base property
    \log_{b}x = \frac{\log_{a}x}{\log_{a}b}
    Thereofre;
    f(x)=\frac {\ln(\sin x)} {\ln e^x} = \frac {\ln(\sin x)} {x}
    So your base is itself a variable? Wow, that is tricky! Yes, it looks to me like you have it reduced properly. Now just use the quotient rule and chain rule.
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