Difference between revisions of "Leibniz rule"
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Latest revision as of 00:57, 5 April 2015
Contents
Definition
A function [math]f:A\rightarrow B[/math] is said to satisfy the Leibniz rule[1][2] if:
[math]f(ab)=af(b)+bf(a)[/math]
It usually involves a lot of abuse of notation and a letter that is an operator.
Example
Take: [math]D:C^\infty_p(\mathbb{R}^n)\rightarrow\mathbb{R}[/math] - a Derivation if it is also [ilmath]\mathbb{R}-[/ilmath]Linear then:
[math]D(fg) = fDg + gDf[/math] - which the reader should recognise as the product rule from calculus.
