Editing Elementary function (section)

=== Basic examples ===
Elementary functions of a single variable {{mvar|x}} include:
* [[Constant function]]s: <math>2,\ \pi,\ e,</math> etc.
* [[Exponentiation#Rational_exponents|Rational powers of {{mvar|x}}]]: <math>x,\ x^2,\ \sqrt{x}\ (x^\frac{1}{2}),\ x^\frac{2}{3},</math> etc.
* [[Exponential function]]s: <math>e^x, \ a^x</math>
* [[Logarithm]]s: <math>\log x, \ \log_a x</math>
* [[Trigonometric function]]s: <math>\sin x,\ \cos x,\ \tan x,</math> etc.
* [[Inverse trigonometric function]]s: <math>\arcsin x,\ \arccos x,</math> etc.
* [[Hyperbolic function]]s: <math>\sinh x,\ \cosh x,</math> etc.
* [[Inverse hyperbolic function]]s: <math>\operatorname{arsinh} x,\ \operatorname{arcosh} x,</math> etc.
* All functions obtained by adding, subtracting, multiplying or dividing a finite number of any of the previous functions<ref>{{cite book|title=Ordinary Differential Equations|date=1985|publisher=Dover|isbn=0-486-64940-7|page=[https://archive.org/details/ordinarydifferen00tene_0/page/17 17]|url-access=registration|url=https://archive.org/details/ordinarydifferen00tene_0/page/17}}</ref>
* All functions obtained by root extraction of a polynomial with coefficients in elementary functions<ref name=":1" />
* All functions obtained by [[function composition|composing]] a finite number of any of the previously listed functions

Certain elementary functions of a single complex variable {{mvar|z}}, such as <math>\sqrt{z}</math> and <math>\log z</math>, may be [[multivalued function|multivalued]]. Additionally, certain classes of functions may be obtained by others using the final two rules. For example, the exponential function <math>e^{z}</math> composed with addition, subtraction, and division provides the hyperbolic functions, while initial composition with <math>iz</math> instead provides the trigonometric functions.