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Bulletin (new series) of the American Mathematical Society
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The differentiation of a function of a function

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1923Publisher:American Mathematical Society (AMS)Journal:Bulletin of the American Mathematical Society, volume 29, page 344 (issn: 0273-0979, eissn: 1088-9485, Copyright policy )
Authors: Carslaw, H. S.;

doi: 10.1090/s0002-9904-1923-03751-8 , 10.2307/3604644

The differentiation of a function of a function

Abstract

If z is a function of y having a differential coefficient at a certain point, and y is a function of x having a differential coefficient at the corresponding point, then z is a function of x having a differential coefficient at that point, and this differential coefficient is given by the formulaThis theorem, thought not always stated so carefully, will be found in all texts on the calculus; but, so far as I am aware, no English writer, not even the most exact, offers a valid proof.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Top 10%
Average
Green
gold