Definition:Elementary Function

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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 of elementary functions include:

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

Also see