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mathematical analysis > calculus > differential calculus > general Leibniz rule

Terme préférentiel

general Leibniz rule

Définition(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)

Concept(s) générique(s)

differential calculus

Traductions

règle générale de Leibniz

français

URI

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

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RDF/XML TURTLE JSON-LD Date de création 02/08/2023, dernière modif. 02/08/2023