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

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Example Sentences

See Examples For:

chain rule

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

To use the chain rule, we again need four quantities— ∂ z/∂ x, ∂ z/dy, dx/dt, and dy/dt:

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

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

The answer is yes, as the generalized chain rule states.

From Textbooks ● Mar. 30, 2016

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