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Thread: 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?
    $\displaystyle y = 2x \log_{10}{\sqrt{x}}$

    $\displaystyle y = x \log_{10}{x}$

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

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


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

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