THE DERIVATIVE OF A FUNCTION AND ITS FUNDAMENTAL PROPERTIES

Boboqulova Durdona Sanjar qizi

First-year student of the Mathematics Department, Faculty of Pedagogy, Shahrisabz State Pedagogical Institute

Keywords: Keywords: derivative, function, rate of change, differentiability, calculus, tangent line, continuity, monotonicity.

---

Abstract

Abstract: This paper explores the concept of the derivative of a function, a cornerstone of differential calculus. The derivative describes how a function changes at any point and serves as a fundamental tool in mathematical modeling, physics, economics, and engineering. The study presents the formal definition of the derivative, rules of differentiation, and key properties such as continuity, monotonicity, and concavity. Applications in real-world contexts are also discussed.

---

References

1. Stewart, J. (2016). Calculus: Early Transcendentals. Cengage Learning.

2. Thomas, G. B., & Finney, R. L. (2010). Calculus and Analytic Geometry. Pearson.

3. Spivak, M. (2008). Calculus. Cambridge University Press.

4. Strang, G. (2016). Calculus. MIT OpenCourseWare.

5. Khan Academy. Derivatives and Differentiation. [https://www.khanacademy.org]

-