\begin{definition}[Definition:Elementary Function]
An '''elementary function''' is one of the following:
* The constant function: $\map {f_c} x = c$ where $c \in \R$
* Powers of $x$: $\map f x = x^y$, where $y \in \R$
* Exponentials: $\map f x = e^x$
* Natural logarithms: $\map f x = \ln x$
* Trigonometric functions: $\map f x = \sin x$, $\map f x = \cos x$
* Inverse trigonometric functions: $\map f x = \arcsin x$, $\map f x = \arccos x$
* 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.
\end{definition}