Derivative at a point

In mathematics, the derivative of a function is a measure of how rapidly the function changes locally when its argument changes.

Formally, the derivative of the function f at a is the limit

$f'(a)=\lim _{h\to 0}{f(a+h)-f(a) \over h}$

of the difference quotient as h approaches zero, if this limit exists. If the limit exists, then f is differentiable at a.