One-sided derivative

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A generalization of the concept of a derivative, in which the ordinary limit is replaced by a one-sided limit. If the following limit exists for a function of a real variable :

then it is called the right (respectively, left) derivative of at the point . If the one-sided derivatives are equal, then the function has an ordinary derivative at . See also Differential calculus.

How to Cite This Entry:
One-sided derivative. G.P. Tolstov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098