Math Doubts

Derivative of Natural Exponential function

Formula

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

The differentiation of natural exponential function is equal to natural exponential function. It is read as the derivative of $e$ raised to the power of $x$ with respect to $x$ is equal to $e^{\displaystyle x}$.

Introduction

Assume, $x$ is a variable, then the natural exponential function is written as $e^{\displaystyle x}$ in mathematical form. The derivative of the $e^{\displaystyle x}$ function with respect to $x$ is written in the following mathematical form.

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

In differential calculus, the derivative of the $e^{\displaystyle x}$ function with respect to $x$ is also written as $\dfrac{d{\,(e^{\displaystyle x})}}{dx}$ and is also written as ${(e^{\displaystyle x})}’$ in simple mathematical form.

Other form

The derivative of the natural exponential function can be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{dq}{\, (e^{\displaystyle q})} \,=\, e^{\displaystyle q}$

$(2) \,\,\,$ $\dfrac{d}{dt}{\, (e^{\displaystyle t})} \,=\, e^{\displaystyle t}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, (e^{\displaystyle y})} \,=\, e^{\displaystyle y}$

Proof

Learn how to derive the differentiation of the natural exponential function from first principle in differential calculus.



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
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