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- General_Leibniz_rule abstract "In calculus, the general Leibniz rule, named after Gottfried Leibniz, generalizes the product rule (which is also known as "Leibniz's rule".) It states that if f and g are n-times differentiable functions, then the nth derivative of the product fg is given bywhere is the binomial coefficient.This can be proved by using the product rule and mathematical induction.With the multi-index notation the rule states more generally:This formula can be used to derive a formula that computes the symbol of the composition of differential operators. In fact, let P and Q be differential operators (with coefficients that are differentiable sufficiently many times) and . Since R is also a differential operator, the symbol of R is given by:A direct computation now gives:This formula is usually known as the Leibniz formula. It is used to define the composition in the space of symbols, thereby inducing the ring structure.".
- General_Leibniz_rule wikiPageExternalLink GeneralizedLeibnizRule.html.
- General_Leibniz_rule wikiPageID "1116115".
- General_Leibniz_rule wikiPageRevisionID "563830474".
- General_Leibniz_rule hasPhotoCollection General_Leibniz_rule.
- General_Leibniz_rule subject Category:Calculus.
- General_Leibniz_rule subject Category:Gottfried_Leibniz.
- General_Leibniz_rule comment "In calculus, the general Leibniz rule, named after Gottfried Leibniz, generalizes the product rule (which is also known as "Leibniz's rule".) It states that if f and g are n-times differentiable functions, then the nth derivative of the product fg is given bywhere is the binomial coefficient.This can be proved by using the product rule and mathematical induction.With the multi-index notation the rule states more generally:This formula can be used to derive a formula that computes the symbol of the composition of differential operators. ".
- General_Leibniz_rule label "General Leibniz rule".
- General_Leibniz_rule label "Regra geral de Leibniz".
- General_Leibniz_rule label "Wzór Leibniza".
- General_Leibniz_rule label "Формула Лейбница (производной произведения)".
- General_Leibniz_rule label "一般のライプニッツの法則".
- General_Leibniz_rule sameAs Leibnizovo_pravidlo.
- General_Leibniz_rule sameAs 一般のライプニッツの法則.
- General_Leibniz_rule sameAs Wzór_Leibniza.
- General_Leibniz_rule sameAs Regra_geral_de_Leibniz.
- General_Leibniz_rule sameAs m.047dm4.
- General_Leibniz_rule sameAs Q2586745.
- General_Leibniz_rule sameAs Q2586745.
- General_Leibniz_rule wasDerivedFrom General_Leibniz_rule?oldid=563830474.
- General_Leibniz_rule isPrimaryTopicOf General_Leibniz_rule.