A história da derivada de Mariana: uma experiência didática

in this paper we tell a story for children and adults designed to introduce the concept of derivative as a quotient of infinitesimals. we report on the understanding of 11 and 12-years old girls about the story and the concept. a brief justification for the use of infinitesimals in the teaching of calculus follows, as well as a description of the context of a freshmen calculus course classroom where this story was used as a worksheet. we challenge the calculus teachers and textbook authors to produce something equally accessible for the introduction of the concept of derivative via the theory of limits.