View source for One-sided derivative

A generalization of the concept of a [[Derivative|derivative]], in which the ordinary limit is replaced by a [[One-sided limit|one-sided limit]]. If the following limit exists for a function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682401.png" /> of a real variable <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682402.png" />:

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682403.png" /></td> </tr></table>

then it is called the right (respectively, left) derivative of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682404.png" /> at the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682405.png" />. If the one-sided derivatives are equal, then the function has an ordinary derivative at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068240/o0682406.png" />. See also [[Differential calculus|Differential calculus]].