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natural exponential function

Exponential function with base e, denoted exp(x) or e^x

Entitystrictly increasing function elementary function exponential functionQ47306354

Also known as exponential function · exp · exp() · exp(x) · e^x · exp x

Instance of: strictly increasing function
, elementary function
, exponential function
+1 more

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted ⁠⁠ or ⁠⁠; the latter is preferred when the argument ⁠⁠ is a complicated expression. It is called exponential because its argument can be seen as an exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent although being of very different nature.

Overview

All data

30 statements · 0% with external sources · numbers in brackets are citations

Different from: exponential function
Definition domain: set of real numbers
Image of function: set of positive real numbers
Uses: Euler's number
exponentiation
Mathematical inverse: natural logarithm relative to: function composition
Defining formula: \frac{\mathrm d}{\mathrm dx}\exp(x)=\exp(x),\quad\exp(0)=1
In defining formula: \exp symbol represents: natural exponential function
\frac{\mathrm d}{\mathrm dx} symbol represents: derivative
Power series expansion: e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots + \frac{x^n}{n!} + \cdots

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15 identifiers linking natural exponential function across the web's reference databases

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Source last edited August 13, 2026. AIDB refreshes this page daily.

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AIDB. (2026). natural exponential function (Q47306354). Retrieved from https://aidb.si/e/natural-exponential-function-Q47306354