The [[derivative]] of a $\log$ of $g(x)$ is the derivative of $g(x)$ over $g(x)$. For a function $f(x) = \ln x$ the derivative is $f'(x) = \frac1x$ In the more general case for a function $f(x) = \ln(g(x))$ the derivative is $f'(x) = \frac{g'(x)}{g(x)}$