# Derivatives of Exponential functions

There are three differential rules for exponential functions and they are used as formulas in differential calculus to find the differentiation of exponential functions.

### Power Rule

$\dfrac{d}{dx}{\, (x^n)} \,=\, nx^{n-1}$

### Constant Base Power Rule

The derivative of a constant base exponential function is equal to the product of the constant base exponential function and natural logarithm of the base.

$\dfrac{d}{dx}{\, (a^x)} \,=\, a^x \ln{a}$

### Natural Power Rule

The derivative of a natural exponential function is equal to the natural exponential function.

$\dfrac{d}{dx}{\, (e^x)} \,=\, e^x$

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.