Definition:Elementary Function

Definition
An elementary function is one of the following:


 * The constant function: $f_c \left({x}\right) = c$ where $c \in \R$


 * Powers of $x$: $f \left({x}\right) = x^y$, where $y \in \R$


 * Exponentials: $f \left({x}\right) = e^x$


 * Natural logarithms: $f \left({x}\right) = \ln x$


 * Trigonometric functions: $f \left({x}\right) = \sin x$, $f \left({x}\right) = \cos x$


 * Inverse trigonometric functions: $f \left({x}\right) = \arcsin x, f \left({x}\right) = \arccos x$


 * All functions obtained by replacing $x$ with any of the functions above, e.g. $f \left({x}\right) = \ln \sin x, f \left({x}\right) = e^{\cos x}$


 * All functions obtained by adding, subtracting, multiplying and dividing any of the above types any finite number of times.