# Exponential function

### From Conservapedia

**Exponential functions** are functions of the form *f*(*s*) = *a*^{s}, 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,

,

where ln*a* is the natural logarithm for *a*.

The transcendental number *e* (2.7182818...) has the property that the derivative of the function *e*^{x} is *e*^{x}, since ln *e* = 1. This function is thus important in the solution of many types of differential equations. *e* is the canonical exponential function.