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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.

 


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