The textbook "DIFFERENTIAL CALCULUS. A Mathematical Analysis for Applied Sciences" is dedicated to all university students in distance or face-to-face programs that require learning Differential Calculus in order to use its contents in Applied Sciences. The relevant contributions of this textbook focus on Pedagogy for the Development of Autonomous Learning together with the logical and complete selection of topics. These topics offer the student the necessary knowledge to achieve the conceptual and applied management of Differential Calculus with command in applied sciences, without including demonstrative processes or theoretical constructions typical of pure mathematics. The methodological design offers the student alternatives in learning to learn and learning autonomously in a logical-analytical-constructive and application process of concepts. The aim of the textbook "DIFFERENTIAL CALCULUS. A Mathematical Analysis for Applied Sciences" is to make the university student learn for himself the fundamental theory of differential calculus as part of a teaching-learning process. This process mainly includes theoretical management and conceptual application oriented towards the socioeconomic and administrative sciences.