skip to main content

Mathematics (thesaurus)

Content language

Home / Explore / Browse / Vocabularies / Mathematics (thesaurus)

mathematical analysis > calculus > differential calculus > general Leibniz rule

Preferred term

general Leibniz rule

Definition(s)

In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if ${\\displaystyle f}$ and ${\\displaystyle g}$ are ${\\displaystyle n}$ -times differentiable functions, then the product ${\\displaystyle fg}$ is also ${\\displaystyle n}$ -times differentiable and its ${\\displaystyle n}$ th derivative is given by

${\\displaystyle (fg)^{(n)}=\\sum _{k=0}^{n}{n \\choose k}f^{(n-k)}g^{(k)},}$

where ${\\displaystyle {n \\choose k}={n! \\over k!(n-k)!}}$ is the binomial coefficient and ${\\displaystyle f^{(j)}}$ denotes the jth derivative of f (and in particular ${\\displaystyle f^{(0)}=f}$ ).

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/General_Leibniz_rule)

Broader concept(s)

differential calculus

In other languages

règle générale de Leibniz

French

URI

http://data.loterre.fr/ark:/67375/PSR-Q3XHL73T-H

Download this concept:

RDF/XML TURTLE JSON-LD Created 8/2/23, last modified 8/2/23