The use and application of differential calculus in university students allows them to develop skills in the approach, analysis, modeling and application of problems involving mathematical knowledge for the solution of problems present in both research projects and in their field of work. Because of that this work has been carried out, in order to provide the student or researcher with a tool that facilitates the understanding and application of differential calculus arccy such as inequality, functions, successions, limit and derivative of functions. Taking into account the above, this book has been designed with the aim of providing the reader with an understanding of these topics that are fundamental and very significant in the teaching and learning processes of sciences and especially, of mathematics