# One-sided derivative

From Encyclopedia of Mathematics

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: http://www.encyclopediaofmath.org/index.php?title=One-sided_derivative&oldid=18307

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098