chain rule


: a mathematical rule concerning the differentiation of a function of a function (such as f [u(x)]) by which under suitable conditions of continuity and differentiability one function is differentiated with respect to the second function considered as an independent variable and then the second function is differentiated with respect to its independent variable

Examples of chain rule in a Sentence

Recent Examples on the Web Honest nodes following the longest-chain rule switch to recognizing the grey and orange blocks as valid, discarding the previously official yellow and green blocks. Timothy B. Lee, Ars Technica, 26 Dec. 2020 The algorithm is called backpropagation because error gradients from later layers in a network are propagated backwards and used (along with the chain rule from calculus) to calculate gradients in earlier layers. Timothy B. Lee, Ars Technica, 18 Dec. 2018

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'chain rule.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

First Known Use

circa 1937, in the meaning defined above

Time Traveler
The first known use of chain rule was circa 1937

Dictionary Entries Near chain rule

Cite this Entry

“Chain rule.” Dictionary, Merriam-Webster, Accessed 19 Jun. 2024.

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