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

By using Chain Rule with $\left({\log}_{b} x\right) ' = \frac{1}{\left(\ln b\right) x}$, we have
$f ' \left(x\right) = \frac{1}{\left(\ln b\right) g \left(x\right)} \cdot g ' \left(x\right) = \frac{g ' \left(x\right)}{\left(\ln b\right) g \left(x\right)}$.