Ecco, DanielMorais, Auricelio Carneiro de2016-08-252021-10-132016-08-252021-10-132016https://repositorio.ufrn.br/handle/123456789/43820Such research proposes to limit the teaching approach and derived in high school, as this is an important tool applications in mathematics itself and in other sciences, avoiding excessive memorizing formulas. The proposal initially part with a history of discovery of the calculus, later presenting the intuitive idea of limit, from the increase in the number of sides of the polygons inscribed and circumscribed to a circle. Then presents the concept of derivative, initially as rate of change, and then, from the tangent line to a curve. Some simple derivation rules are presented. Applications range, mathematics, maximum and minimum problems, maximum volume with minimum area and how to get maximum profit. Already in chemistry, it is the speed of the reactions and behavior of volume versus pressure. Physics is fruitful field of applications ranging from the speed and acceleration, through the work and power, to determine the amount of electrical charges and electromagnetic energy. The population count and the amount of blood flow in the arteries / veins are examples where the derivative is used.openAccessMatemática; Aplicações do Cálculo; Ensino Médio.postGraduateThesis