The book "Typical calculations in higher mathematics: educational method . allowance: at 3 h. H. 2: Differential calculus of functions of many permutations by J. A. Black represents a unique and valuable resource for undergraduates, graduate students, and anyone seeking to deepen their knowledge of higher mathematics. This manual, which is the second part of an extensive three-volume edition, focuses on the differential calculus of functions of several variables, making it an indispensable tool for the study and practical application of mathematical concepts. In the first part of the book, the author introduces readers to the world of differential calculus, starting with the basics and gradually moving to more complex topics. Chernyak masterfully explains key concepts such as partial derivatives, gradients, differentials, and extremums of functions of several variables. Each topic is accompanied by illustrative examples and typical tasks, which allows readers not only to learn theoretical material, but also to apply it in practice. This makes the manual especially useful for students of technical and natural sciences specialties, as well as for all who are preparing for exams in higher mathematics. The book will be interesting not only for students, but also for teachers who are looking for high-quality teaching materials for their classes. It can be a great addition to math training courses, as well as being used for self-study. Chernyak appeals to readers who seek not only to memorize the formulas, but also to understand how and why they work, which is the basis for successfully mastering more complex mathematical disciplines. The topics raised in the book cover a wide range of issues related to differential calculus. The author focuses on the importance of understanding multidimensional functions and their properties, which is a key aspect in areas such as physics, economics and engineering. The book also touches on the application of mathematical methods to real-world problems, which makes the material more relevant and interesting for readers. Writing style . A. Blackberries are clear and accessible, which makes it easy to perceive even the most complex concepts. It uses many real-life examples to help readers see the practical application of the material being studied. Cherniak is also known for his other work in the field of higher mathematics, and his experience and in-depth knowledge in this field make his manual particularly valuable.. If you are looking for a high-quality tutorial on higher mathematics, which will help you not only understand the theory, but also learn to solve practical problems, the book "Type calculations in higher mathematics" will become your reliable companion. This publication is ideal for students, graduate students and anyone who wants to deepen their knowledge in the field of mathematical analysis. Do not miss the opportunity to get acquainted with this unique work, which will open up new horizons in the world of higher mathematics!