View source for Exponential function

[[Image:Exp.png|right|pxl=200|thumb|exponential functions]]
'''Exponential functions''' are [[function]]s of the form <math>f(s)=a^{s}</math>, where ''a'' is a [[constant]] and ''s'' is a [[complex number]]. They are based on the mathematical [[operation]] of [[exponentiation]].

The derivative of an exponential function is,

<math>\frac{d}{dx}a^{x}=a^{x}\ln{a}</math>,

where <math>\ln{a}</math> is the [[natural logarithm]] for ''a''.

The [[transcendental number]] ''[[e]]'' (2.7182818...) has the property that the [[Derivative (calculus)|derivative]] of the function ''e''<sup>''x''</sup> is ''e''<sup>''x''</sup>, since ln ''e'' = 1.  This function is thus important in the solution of many types of differential equations. ''e'' is the canonical exponential function.

[[Category:Mathematics]]