Derivative at a point: Difference between revisions

Revision as of 20:59, 23 November 2007

In mathematics, derivative of a function is a measure of how rapidly the function changes locally when its argument changes.

Formally, the derivative of the function f at a is the limit

f'(a)=\lim _{h\to 0}{f(a+h)-f(a) \over h}

of the difference quotient as h approaches zero, if this limit exists. If the limit exists, then f is differentiable at a.

@@ Line 1: / Line 1: @@
 In [[mathematics]], derivative of a [[Mathematical function|function]] is a measure of how rapidly the function changes locally when its argument changes.
-Formally, the '''derivative''' of the function ''f'' at ''a'' is the [[limit (mathematics)|limit]]
+Formally, the '''derivative''' of the function ''f'' at ''a'' is the [[Limit of a function|limit]]
 :<math>f'(a)=\lim_{h\to 0}{f(a+h)-f(a)\over h}</math>
 of the difference quotient as ''h'' approaches zero, if this limit exists.  If the limit exists, then ''f'' is ''differentiable'' at ''a''.