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

See Examples For:

chain rule

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

This notation for the chain rule is used heavily in physics applications.

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

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

From Textbooks ● Mar. 30, 2016

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