chain rule

chain rule
noun
: a mathematical rule concerning the differentiation of a function of a function (as f[u(x)]) by which under suitable conditions of continuity and differentiability one function is differentiated with respect to the second considered as an independent variable and then the second function is differentiated with respect to its independent variable

if v=u2 and u=3x2+2 the derivative of v by the chain rule is 2u(6x) or 12x(3x2+2)

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Math.
the theorem that defines the method for taking the derivative of a composite function.
[1860-65]

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chain rule noun
1. An arithmetical rule, so called from the terms of the problem being stated as equations, and connected, as if by a chain, so as to obtain by one operation the same result as would be obtained by a number of different operations in simple proportion
2. The rule for solving problems by compound proportion
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Main Entry:chain

Useful english dictionary. 2012.

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  • Chain rule — For other uses, see Chain rule (disambiguation). Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation …   Wikipedia

  • Chain rule (disambiguation) — Chain rule may refer to: Chain rule in calculus: Cyclic chain rule, or triple product rule: Chain rule (probability) …   Wikipedia

  • Chain rule (probability) — In probability theory, the chain rule permits the calculation of any member of the joint distribution of a set of random variables using only conditional probabilities. Consider an indexed set of sets . To find the value of this member of the… …   Wikipedia

  • Chain rule for Kolmogorov complexity — The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: H(X,Y) = H(X) + H(Y | X) That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever… …   Wikipedia

  • chain rule — noun Date: circa 1937 a mathematical rule concerning the differentiation of a function of a function (as f [u(x)]) by which under suitable conditions of continuity and differentiability one function is differentiated with respect to the second… …   New Collegiate Dictionary

  • chain rule — Math. the theorem that defines the method for taking the derivative of a composite function. [1860 65] * * * …   Universalium

  • Chain — (ch[=a]n), n. [F. cha[^i]ne, fr. L. catena. Cf. {Catenate}.] 1. A series of links or rings, usually of metal, connected, or fitted into one another, used for various purposes, as of support, of restraint, of ornament, of the exertion and… …   The Collaborative International Dictionary of English

  • Chain belt — Chain Chain (ch[=a]n), n. [F. cha[^i]ne, fr. L. catena. Cf. {Catenate}.] 1. A series of links or rings, usually of metal, connected, or fitted into one another, used for various purposes, as of support, of restraint, of ornament, of the exertion… …   The Collaborative International Dictionary of English

  • Chain boat — Chain Chain (ch[=a]n), n. [F. cha[^i]ne, fr. L. catena. Cf. {Catenate}.] 1. A series of links or rings, usually of metal, connected, or fitted into one another, used for various purposes, as of support, of restraint, of ornament, of the exertion… …   The Collaborative International Dictionary of English

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