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Math Help - Taking derivative of a function times a log

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    Taking derivative of a function times a log

    y=2xlog base 10(rootx)
    What are the proper steps for solving this?
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    Quote Originally Posted by ajcadoo View Post
    y=2xlog base 10(rootx)
    What are the proper steps for solving this?
    y = 2x \log_{10}{\sqrt{x}}

    y = x  \log_{10}{x}

    y = x \cdot  \frac{\ln{x}}{\ln{10}}

    y = \frac{1}{\ln{10}}\left(x  \ln{x}\right)


    y' = \frac{1}{\ln{10}}\left(x  \cdot \frac{1}{x} + \ln{x}\right)

    y' =  \frac{1}{\ln{10}}\left(1 + \ln{x}\right) =  \frac{1+\ln{x}}{\ln{10}}
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