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### Lateral derivatives

The derivative of *f* (*x*) is defined as both limits from the left and from right to the point *x* = *a*

and

for *h* > 0. These conditions are required and sufficient for the derivate *f* ′(*a*) to exist, where , and means the the function *f* (*x*) is differentiable in *x* = *a*.

##### Example 1

The lateral derivatives of the function *f* (*x*) = | *x* | in *x* = 0 are

This function cannot be differentiated at this point, as the tangent lines from left and from right are not equal.