# Differentiation Rules for Exponential Functions

In this tutorial we discuss the basic differentiation formulas of exponential functions.

1. $\frac{d}{{dx}}{a^x} = \frac{1}{{x\ln a}},\,\,\,a > 0,\,\,\,a \ne 1$

2. $\frac{d}{{dx}}{e^x} = {e^x}$

Now the general exponential formulae with any function are of the form

1. $\frac{d}{{dx}}{a^{f\left( x \right)}} = \frac{1}{{f\left( x \right)\ln a}}\frac{d}{{dx}}f\left( x \right),\,\,\,a > 0,\,\,\,a \ne 1$

2. $\frac{d}{{dx}}{e^{f\left( x \right)}} = {e^{f\left( x \right)}}\frac{d}{{dx}}f\left( x \right)$