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mathematical analysis > real analysis > chain rule

mathematical analysis > calculus > differential calculus > chain rule

Preferred term

chain rule

Definition(s)

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions $f$ and $g$ in terms of the derivatives of $f$ and $g$ . More precisely, if ${\\displaystyle h=f\\circ g}$ is the function such that ${\\displaystyle h(x)=f(g(x))}$ for every $x$ , then the chain rule is, in Lagrange's notation,

${\\displaystyle h'(x)=f'(g(x))g'(x).}$

or, equivalently,

${\\displaystyle h'=(f\\circ g)'=(f'\\circ g)\\cdot g'.}$

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

Broader concept(s)

Related concept(s)

Faà di Bruno's formula

In other languages

théorème de dérivation des fonctions composées

French
règle de dérivation en chaîne
règle de la chaîne

URI

http://data.loterre.fr/ark:/67375/PSR-HLD5248R-P

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