# Courses in Math - Definition - Derivative - taketechease

## Derivative. Definition.

This page contains definition of derivative. Derivative of a function is a one of the most important mathematical properties. It represents a rate of change of a function with respect to an independent variable. The differential calculus's fundamentals are based on the derivative.

Let's consider a function f(x) defined in a given range γ. Next move from the x = x_{0} point with the step δx > 0 or δx < 0 such that the new value of x = x_{0} + δx is still within the range γ. Then the value of the f function changes from f(x_{0}) to f(x_{0} + δx). If the the limit of the expression

[f(x_{0} + δx) - f(x_{0})]/δx

when

δx tends to 0

exists it is called the derivative of f function upon variable x in the x_{0} point.

Much more about derivatives you can find at the page derivatives - analytical examples.