The book “Differential Calculus of Functions of Several Variables: Methodical Guidelines for Performing Control Work” is an indispensable assistant for students and teachers seeking to understand more deeply the complex concepts of mathematical analysis. The team of authors, who gathered their knowledge and experience, created this work in order to facilitate the process of studying and performing control works on differential calculus, which is the fundamental section of higher mathematics. The book discusses the basic principles and methods of differential calculus of functions of several variables, which makes it especially useful for students of mathematical, engineering and economic specialties. Here you will find detailed explanations of the theoretical foundations, as well as practical tasks that will help to consolidate the knowledge gained. Each section of the book is thought out in such a way that the reader can not only absorb the material, but also apply it in practice, which is especially important for the successful performance of control works. Who can like this book? First of all, it will be useful for students studying in the faculties of mathematics, physics, engineering and economics . If you are just starting your path in higher mathematics or already have some experience, but want to improve your skills, this guide will be a real find for you. The book will also be of interest to teachers who are looking for high-quality teaching materials for their students, as well as to anyone who wants to refresh their knowledge in the field of differential calculus. The topics raised in the book cover a wide range of issues related to differential calculus. The authors explain in detail how to find partial derivatives, how to apply differentiation rules to the functions of several variables, and how to solve problems related to extremities of functions. In addition, the book discusses the applications of differential calculus in various fields of science and technology, which allows the reader to see the practical significance of the material being studied. One of the features of this book is its accessible and understandable style of presentation. The authors aim to make complex mathematical concepts more accessible to perception, using illustrative examples and illustrations. This makes the material not only more interesting, but also greatly simplifies the learning process. The book also includes a variety of problem-solving tasks, allowing the reader to independently test their knowledge and skills. If you are looking for other books on mathematics that will help you in the study of differential calculus, pay attention to such names as "