Definition:Elementary Function

Definition
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.