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Compute the derivative of x (sin (log x) – cos (log x))

by RoRi

Compute the derivative of the function

    \[ f(x) = x ( \sin (\log x) - \cos (\log x)). \]

Using the chain and product rules we compute,

    \begin{align*} f'(x) &= (\sin (\log x) - \cos (\log x)) + x \left( \frac{\cos (\log x)}{x} + \frac{\sin (\log x)}{x} \right)\\ &= 2 \sin (\log x). \end{align*}

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