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Compute the derivative of log(x2 log x)

Compute the derivative of

    \[ f(x) = \log(x^2 \log x). \]


Using the chain rule (and the product rule on x^2 \log x) we have

    \begin{align*}  f'(x) &= \left( \frac{1}{x^2 \log x} \right) \left(2x \log x + \frac{x^2}{x} \right) \\  &= \frac{2}{x} + \frac{1}{x \log x}  \end{align*}

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