2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60070This article exemplifies a novel approach to the teaching of introductory differential calculus using the modern notion of ``infinitesimal'' as opposed to the traditional approach using the notion of ``limit''. I illustrate the power of the new approach with a discussion of the derivatives of the sine and cosine functions.LaTeX; 19 pp, 6 figsGeneral Mathematics00-01; 97-01text