# What is the derivative of f(x)=ln(g(x)) ?

The answer would be $f ' \left(x\right) = \frac{1}{g} \left(x\right) \cdot g ' \left(x\right)$ or it can be written as $f ' \left(x\right) = \frac{g ' \left(x\right)}{g} \left(x\right)$.
$F \left(x\right) = f \left(g \left(x\right)\right)$ then $F ' \left(x\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$
The derivative of $h \left(x\right) = \ln \left(x\right)$ is $h ' \left(x\right) = \frac{1}{x}$.