Natural Exponential function

Function

$e^{\displaystyle x}$

Introduction

$e^{\displaystyle x}$ $\,=\,$ $1$ $+$ $\dfrac{x}{1!}$ $+$ $\dfrac{x^2}{2!}$ $+$ $\dfrac{x^3}{3!}$ $+$ $\dfrac{x^4}{4!}$ $+$ $\cdots$ $+$ $\infty$

Graph

Domain

Range

$e^{\displaystyle x}$ $\,=\,$ $\displaystyle \lim_{n\,\to\,\infty}{\Big(1+\dfrac{x}{n}\Big)^{\displaystyle n}}$

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

$\displaystyle \int{e^{\displaystyle x}}\,dx \,=\, e^{\displaystyle x}+c$