# What is the derivative of f(x)=b^x ?

This is the exponential function of base $b$ (where $b > 0$ should be assumed). It can be thought of as ${b}^{x} = {e}^{x \ln \left(b\right)}$, so that, using the Chain Rule (See Chain Rule ) and the fact that $\left({e}^{x}\right) ' = {e}^{x}$ (see Exponentials with Base e ) yields $\left({b}^{x}\right) ' = {e}^{x \ln \left(b\right)} \setminus \times \ln \left(b\right) = {b}^{x} \setminus \times \ln \left(b\right)$