chain rule

American  

noun

Mathematics.

1. the theorem that defines the method for taking the derivative of a composite function.

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chain rule British  

noun

1. maths a theorem that may be used in the differentiation of the function of a function. It states that d u /d x = (d u /d y )(d y /d x ), where y is a function of x and u a function of y

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Etymology

Origin of chain rule

First recorded in 1860–65

Example Sentences

This proves the chain rule at t = t0; the rest of the theorem follows from the assumption that all functions are differentiable over their entire domains.

From Textbooks • Mar. 30, 2016

Tree diagrams are useful for deriving formulas for the chain rule for functions of more than one variable, where each independent variable also depends on other variables.

From Textbooks • Mar. 30, 2016

At this point we provide a list of derivative formulas that may be obtained by applying the chain rule in conjunction with the formulas for derivatives of trigonometric functions.

From Textbooks • Mar. 30, 2016

It is not absolutely necessary to memorize these as separate formulas as they are all applications of the chain rule to previously learned formulas.

From Textbooks • Mar. 30, 2016

Use differentiation, applying the chain rule as necessary, to find an equation that relates the rates.

From Textbooks • Mar. 30, 2016