THE IMPORTANCE OF DERIVATIVES IN ECONOMIC AND PHYSICAL PROCESSES: THEORY AND PRACTICE

Abstract

This article explores the application areas of derivatives, one of the key concepts in mathematical analysis, in economic and physical processes. The derivative is used as a powerful mathematical tool for studying the relationship between changing quantities, analyzing dynamic systems, determining the rate of changes within them, and making optimal decisions. In economics, the derivative is crucial for analyzing the achievement of maximum or minimum function values, while in physics, it is vital for determining velocity, acceleration, and similar parameters. The article explains the theoretical foundations of derivatives (first, second, and nth-order derivatives), their role in analyzing economic indicators, and the mathematical modeling of physical laws, along with practical examples. This work connects theory with practice, revealing the efficiency of applying derivatives in real-world processes.