2025-09-182025-09-182025-07-07https://repositorio.ifal.edu.br/handle/123456789/1248Differential calculus represents one of the most significant discoveries in mathematics and science. Its development occurred gradually, with contributions from several thinkers throughout history, being largely attributed to the works of Gottfried Leibniz and Isaac Newton. Although both were polymaths, they had different perspectives: Leibniz approached the topic from a purely mathematical standpoint, seeking methods to determine the slope of tangent lines, while Newton focused on calculating the instantaneous velocity of a moving object. This work aims to present the development of differential calculus from both perspectives, ranging from its applications in analytic geometry to its relevance in kinematics. Furthermore, the formal concept of the derivative, its main rules, and applications are discussed, highlighting its importance as a tool for analyzing the motion of bodies.ptMatemática - LicenciaturaMatemática - HistóriaCálculo diferencialDerivadaCinemáticaDifferential calculusDerivativeHistory of mathematicsKinematicsTrabalho de Conclusão de CursoCIENCIAS EXATAS E DA TERRA::MATEMATICA