Exponential function

exponential functions

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,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}a^{x}=a^{x}\ln{a}} ,

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. This function is thus important in the solution of many types of differential equations. e is the canonical exponential function.