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

Property vi. can be proved using the chain rule.

From Textbooks • Mar. 30, 2016

The same thing is true for multivariable calculus, but this time we have to deal with more than one form of the chain rule.

From Textbooks • Mar. 30, 2016

In particular, the constant multiple rule, the sum and difference rules, the product rule, and the chain rule all extend to vector-valued functions.

From Textbooks • Mar. 30, 2016

Instead, we use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

From Textbooks • Mar. 30, 2016

In single-variable calculus, we found that one of the most useful differentiation rules is the chain rule, which allows us to find the derivative of the composition of two functions.

From Textbooks • Mar. 30, 2016