Math Doubts

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.

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

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more