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Math Help - Derivative of logarithmic function.

  1. #1
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    Derivative of logarithmic function.

    Hi guys I am working on a derivative problem and think I have the answer but my algebra with logs is embarrassing so I'm struggling to simplify my answer. Here it is:

    f(x)= \sqrt{\log_{5} x+1}-1

    So,  f'(x)= \frac{d}{dx}(\frac{\ln(x)}{\ln5}+1)^\frac{1}{2}+0 (d/dx(-1)=0)

    Then chain rule:

    \frac{1}{2}\times(\frac{\ln(x)}{\ln(5)}+1)^\frac{-1}{2}\times\frac{1}{x\ln(5)}

    and my answer is:

    \frac{1}{2\times\sqrt{log_{5}x+1}}\times\frac{1}{x  \ln(5)}

    How can I simplify this? >implying its correct
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  2. #2
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    Re: Derivative of logarithmic function.

    It is correct. Just write it as a single fraction (i.e. get rid of the times symbol between the fractions) and that will be enough
    Thanks from camjerlams
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