Application of the derivative function of a single variable in mathematics and physics courses in higher educational institutions
DOI:
https://doi.org/10.15587/2519-4984.2025.345337Keywords:
derivative, differentiation rules, tangent line, extremum, mathematical analysis, velocity, acceleration, physical lawsAbstract
The article explores the theoretical foundations of the concept of the derivative, as well as its geometric and physical meaning, since the derivative is an important notion that shows how quickly a quantity changes. In mathematics, it represents the slope of the tangent to a curve, while in physics it reflects the rate of a process.
The article examines how exactly the derivative is used in mathematics and physics, and why it is considered an essential tool for studying various phenomena, as understanding derivatives is necessary for learning mathematical and physical disciplines.
It explains the concept of the derivative, how it can be represented graphically, and its significance in physics. Attention is given to the use of derivatives for solving mathematical problems: analyzing the behavior of functions, constructing tangents, finding maximum and minimum values, interpreting graphs, and resolving indeterminate forms using L’Hôpital’s rule. The article highlights the applications of derivatives in physics, particularly for describing motion, determining instantaneous velocity and acceleration. It also emphasizes that derivatives are used to formulate the laws of dynamics (such as Newton’s second law) and to describe various physical phenomena, including oscillations and radioactive decay.
The text underscores that understanding derivatives is essential for mastering engineering and physical sciences, as well as mathematics and physics in general. Derivatives are also used in studying theoretical mechanics, material resistance, hydraulic and hydrodynamic equations, thermal engineering, and electrical engineering.
Finally, it explains why students need to understand derivatives, as they form the foundation for studying mathematics and applying it in technical sciences and engineering
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Copyright (c) 2025 Tetiana Voііtik, Serhii Kyrylov, Tetiana Kopeykina, Olha Shurlo
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