### 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.

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|.

The function is not differentiable at x = 0.

The function is not differentiable at x = 0.

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