espanolSe presentan algunos metodos que se desarrollaron a traves de la historia para encontrar derivadas desde Apolonio de Perga hasta Cauchy. A partir de estos, se plantean representaciones semioticas que permiten abordar la derivada (numerico, algebraico, formal, geometrico, infinitesimal, aproximacion afin local, variacional y computacional). Encontrando que el concepto como se ensena en la actualidad no coincide con el desarrollo de su genesis y que una forma de comprender el concepto de derivadas a partir de uso de tratamientos y conversiones de registros de representacion. EnglishSome methods that were developed throughout history to find derivatives from Apolonio de Perga to Cauchy are presented, then itineraries are proposed for the introduction of the derivative in the curriculum: addressing positions of the theory of Action, Process, Object and Scheme (APOE) and the tools proposed by the known as the Onto-Semiotic Approach (OSA), for elements of the derivative before the limit and limits before derivatives. From these, semiotic representations are proposed that allow to approach the derivative (numerical, algebraic, formal, geometric, infinitesimal, local, variational and computational related approximation). Finding that the concept as taught today does not coincide with the development of its genesis and that a way of understanding the concept of derivatives from the use of treatments and conversions of registers of representation.