One-Sided Derivative

Left-Hand Derivative

Left-Hand Derivative

Right-Hand Derivative

A function is differentiable at a point if and only if it is differentiable from the left and right side and these derivatives coincide.

Derivative of Piecewise Functions

With piecewise functions, it is necessary to study the derivatives at the points of lateral separation of the different pieces.

Study the differentiability of the function f (x)= |x|.

Derivative of Piecewise Functions

Derivative of a Piecewise Function

Derivative of a Piecewise Function

The function is not differentiable at x = 0.

Piecewise Function


Piecewise Function

Derivative of a Piecewise Function

Derivative of a Piecewise Function

The function is not differentiable at x = 0.

Piecewise Function