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

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

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 a tree diagram and the chain rule to find an expression for ∂ u.

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

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