Derivative at a point: Difference between revisions
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imported>Joe Quick m (subpages) |
imported>Jitse Niesen (remove "See also" section after subsuming it in the "Related Articles" subpage) |
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:<math>f'(a)=\lim_{h\to 0}{f(a+h)-f(a)\over h}</math> | :<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''. | of the difference quotient as ''h'' approaches zero, if this limit exists. If the limit exists, then ''f'' is ''differentiable'' at ''a''. | ||
Revision as of 07:37, 22 October 2008
In mathematics, the 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
of the difference quotient as h approaches zero, if this limit exists. If the limit exists, then f is differentiable at a.