A derivada segundo Silvanus Thompson

Abstract

The purpose of this project is to show a possibility of approach of the derivatives to the high school students, using a historical report by how the study of the Calculus was developed, more specifically, of the derivative over time, as well as motivating problems that have boosted such content. Definitions are presented involving derived with applications in the geometric-algebraic process as in the case of tangent line, or at physics area, through the speed and acceleration, all of them associated with the rate of change concept. When defining the derivative employability, it makes a link between the derivative and its application with the high school contents, in which they can be explored relative topics with the studies of functions: as growth and decrease, maximum and minimum points, and also, investigate through visual analysis, parameters relevant to the function. Also analyzed how Silvanus Thompson developed the reasoning of the resolution of some derivatives, such as of polynomials, sine, cosine and tangent, being that this study differs from the traditional way to obtain the derivative, once it does not use the limits for its achievement. Finally, is presented demonstrations realized by Silvanus Thompson, of how to understand addition, product, quotient and the chain rule. Is showing at Gutemberg Project, from public domain, Calculus Made Easy book.