Editing Chain rule (section)

== History ==

The chain rule seems to have first been used by [[Gottfried Wilhelm Leibniz]]. He used it to calculate the derivative of <math>\sqrt{a + bz + cz^2}</math> as the composite of the square root function and the function <math>a + bz + cz^2\!</math>. He first mentioned it in a 1676 memoir (with a sign error in the calculation).<ref>{{Cite journal |last=Child |first=J. M. |date=1917 |title=THE MANUSCRIPTS OF LEIBNIZ ON HIS DISCOVERY OF THE DIFFERENTIAL CALCULUS. PART II (Continued) |url=https://www.jstor.org/stable/27900650 |journal=The Monist |volume=27 |issue=3 |pages=411–454 |doi=10.5840/monist191727324 |jstor=27900650 |issn=0026-9662}}</ref> The common notation of the chain rule is due to Leibniz.<ref name="OHR">{{cite journal|url= https://scholarworks.umt.edu/tme/vol7/iss2/10/ |title=A Semiotic Reflection on the Didactics of the Chain Rule |journal=The Mathematics Enthusiast |year=2010 |volume=7 |pages=321–332 |issue=2 |first1=Omar Hernández |last1=Rodríguez |first2=Jorge M. |last2=López Fernández |doi=10.54870/1551-3440.1191 |s2cid=29739148 |access-date=2019-08-04|doi-access=free }}</ref> [[Guillaume de l'Hôpital]] used the chain rule implicitly in his ''[[Analyse des infiniment petits]]''. The chain rule does not appear in any of [[Leonhard Euler]]'s analysis books, even though they were written over a hundred years after Leibniz's discovery.{{citation needed|date=September 2022}}. It is believed that the first "modern" version of the chain rule appears in Lagrange's 1797 ''Théorie des fonctions analytiques''; it also appears in Cauchy's 1823 ''Résumé des Leçons données a L’École Royale Polytechnique sur Le Calcul Infinitesimal''.<ref name="OHR"/>