Похідна як засіб моделювання динамічних процесів

Abstract

The paper considers the derivative as one of the main tools of mathematical analysis for modeling real processes that change over time. It is shown that the use of derivatives makes it possible to describe the rate and nature of changes in physical, economic, and technical quantities, as well as to analyze process dynamics and determine optimal parameters of their behavior. Based on functional relationships and their derivatives, examples of mechanical motion, growth processes, and optimization problems are studied. The obtained results confirm the effectiveness of derivatives in quantitative analysis and prediction of real system behavior.