# 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.

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