The textbook "DIFFERENTIAL CALCULUS. A Mathematical Analysis for Applied Sciences" is dedicated to all university students in distance or face-to-face programs who need to learn Differential Calculus to use its contents in Applied Sciences. The relevant contributions of this textbook focus on the 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 handling of Differential Calculus with mastery in applied sciences, without including demonstrative processes or theoretical constructions typical of pure mathematics. The methodological design offers the student alternatives to learn and learn autonomously in a logical-analytical-constructive process and application of concepts. The textbook "DIFFERENTIAL CALCULUS. A mathematical analysis for applied sciences" aims for university students to learn by themselves the fundamental theory of differential calculus as part of a teaching-learning process. This process mainly includes theoretical management and conceptual application oriented to socioeconomic and administrative sciences.