Definition of Derivative

What is the definition of derivative?

The definition of derivative is shown below. First of all if y = f(x) is a function. The derivative of y with respect to x is the function whose value at x is the limit, shown in the picture of definition of derivative below, provided this limit exists.

If this limit exists for each x in an open interval I, then we say that f is differentiable on I.

where

Derivative notations

The derivative is also denoted by:

The process of taking a derivative is called differentiation. Derivatives are used widely in calculus along with the differentiation process and the integration process.