@article {MATHEDUC.06219746,
author = {Campistrous, Luis Augusto and L\'opez Fern\'andez, J\'orge M. and Rizo Cabrera, Celia},
title = {History and didactics: the case of the text by L'H\^opital {\it Analyse des infiment petit deslignes courbes}. (Historia y did\'actica: el caso del escrito de L'H\^opital {\it Analyse des infiniment petits pour l'intelligence des lignes courbes}.)},
year = {2011},
journal = {Epsilon [electronic only]},
volume = {28},
number = {77},
issn = {1131-9321},
pages = {51-64},
publisher = {Sociedad Andaluza de Educaci\'on Matem\'atica ``Thales'', Centro Documentaci\'on ``Thales'', Universidad de C\'adiz, Puerto Real (C\'adiz)},
abstract = {Summary: Nowhere in L'H\^opital's famous textbook is the chain rule (the rule for differentiating the composition of two functions) proved. It is neither proved or justified in any of Euler's analysis books. In this article, the authors contend that this rule is obvious in the language of infinitesimals and differentials, common in L'H\^opital's times. Such a circumstance makes the chain rule so clearly valid as to require no explicit proof. Furthermore, the rule was conceived as an algorithm for calculating derivatives of functions that are obtained from other differentiable functions by substitution of variables that are also differentiable. It is an anachronism to imagine that the chain rule as used in L'H\^opital's and Euler's writings has any relation with the composition of functions. In the history of mathematics, the composition of functions is defined at least two centuries after the publication of L'H\^opital's work. Finally, arguments are presented to document the didactic advantage of teaching the chain rule as an algorithm to find the derivative (difference) of a function that is obtained from a differentiable function by substituting a differentiable variable.},
msc2010 = {A30xx (I40xx)},
identifier = {2013f.00050},
}