LA DERIVADA: UN PUNTO DE VISTA HIST 3RICO

El estudio que se muestra en este art\uedculo tiene como prop\uf3sito describir los significados que los matem\ue1ticos le otorgaron a lo largo de la historia, al objeto derivada. El estudio se enmarca en la teor\ueda sist\ue9mica denominada Enfoque Ontosemi\uf3tico de la Cognici\uf3n e Instrucci\uf3n Matem\ue1tica (EOS). Esta descripci\uf3n permite ensanchar las concepciones del didactista y orientar el dise\uf1o de actividades y tareas que contribuyan a la construcci\uf3n del conocimiento que se busca en los estudiantes (Tall, 1991).Adem\ue1s es el punto de partida para la construcci\uf3n de unidades did\ue1cticas (Guti\ue9rrez y Valdiv\ue9, 2012). Los actores sociales objeto de estudio son los libros de texto. Entre los hallazgos podr\uedamos indicar que los matem\ue1ticos otorgaron diversos significados al objeto derivada: incrementos infinitesimales, fluyentes y fluxiones, razones primeras y \ufaltimas, l\uedmite de un cociente incremental, y a finales del siglo XIX se da la definici\uf3n anal\uedtica que se utiliza en la actualidad. Palabras claves del Autor: Derivada, an\ue1lisis epistemol\uf3gico, EOS.ABSTRACTTHE DERIVATIVE: A HISTORICAL POINT OF VIEW The research in this article attempts to describe the significance given by mathematicians throughout history to the derivative. The study is based on a systemic theory known as the onto-semiotic approach of Cognition and Instruction Mathematics (EOS). This allows the educator to both broaden conceptions of and guide the designs of activities and tasks that contribute to the construction of knowledge in students (Tall, 1991). It is also the starting point for the construction of teaching units (Gutierrez and Valdiv\ue9, 2012). To this end,relevant textbooks are studied. Findings indicate that mathematicians gave different meanings to the concept of the derivative: infinitesimal increments, flowing and fluxions, first and last reasons, limits of a different quotient, and since the late nineteenth century, the analytical definition that is used today. Key words: Derivative, epistemological analysis, EOS.