# Definition:Elementary Function

## Definition

An elementary function is one of the following:

• Powers of $x$: $\map f x = x^y$, where $y \in \R$
• All functions that are compositions of the above, for example $\map f x = \ln \sin x$, $\map f x = e^{\cos x}$
• All functions obtained by adding, subtracting, multiplying and dividing any of the above types any finite number of times.

## Examples

Examples of elementary functions include:

$2 x - \ln x + \dfrac {e^{\sin x} } x$
$\paren {\arccos x}^2 + \dfrac {e^{x^2 + 2x + 1} } {\sqrt {3 x} } - \map \ln {\ln 4 x}$