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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.