Production function and its application: training. -method. Handbook" is a fascinating and informative publication created by a team of authors, which will become an indispensable assistant for students, teachers and anyone interested in mathematics and its practical aspects. This manual not only explains the derivative theory, but also opens the door for the reader to the world of its application in various fields of science and technology. At the heart of the book is the concept of a derivative function, one of the basic concepts of mathematical analysis. The authors masterfully explain what a derivative is, how it can be calculated and what tasks it helps to solve. But this is not just a dry theory; the manual is saturated with real-life examples that make the material more accessible and understandable. The reader will be able to see how the derivative is used in physics to describe speed and acceleration, in economics to analyze price changes, and in biology to model population growth. This makes the book especially valuable for those who want to connect theory with practice and see how mathematics permeates all aspects of our lives. The book will be of interest not only to students of mathematical and technical specialties, but also to teachers who are looking for new approaches to explaining complex concepts. It is suitable for both high school students preparing for exams, and for university students studying mathematical analysis. If you are passionate about mathematics, physics or economics, this guide will be a real find for you. The topics that are raised in the book cover a wide range of issues. The authors discuss not only the main properties of the derivative, but also its geometric meaning, the rules of differentiation, as well as the applications of the derivative in various spheres. The reader will be able to learn about such important concepts as extremities of functions, inflection points and their meaning, as well as how the derivative helps in optimizing processes and solving practical problems. This makes the manual not just educational material, but also a real source of inspiration for those who want to deepen their knowledge and skills. The style of the authors is clear and accessible, which makes even the most complex topics understandable to a wide audience. Each section of the book is structured in such a way that the reader can easily follow the logic of the presentation, and practical tasks will help to consolidate the knowledge gained. This manual will be an excellent addition to any course in mathematical analysis and will be useful both for self-study and for use in the educational process. If you are looking for literature that will help you understand the derivative function and its application, this manual is your ideal choice. It will become a reliable companion on the way to understanding mathematics and its role in the modern world. Do not miss the opportunity to discover new horizons of knowledge and understand how a derivative can change your perception of the surrounding reality. Production function and its application: training. -method. The textbook is not just a textbook, but a real find for anyone who aspires to knowledge and wants to understand how mathematics helps solve real problems.