2.4. Derivative 2.4.1. Derivative Definition

Let function defined on interval .

Let the number . Give x increment Δx so that . Incrementing the argument Δx will cause the function to increment . The limit (if it exists) of the ratio of the increment of the function Δy to the increment of the argument Δx as Δx → 0 is called the derivative of the function and is denoted by i.e.

At the same time, the function itself called differentiable .
The following symbols are also used to denote a derivative: .