Derivatives: A Comprehensive Study of Rate of Change

In mathematics, derivatives are the rate of change of a function with respect to a variable, and they are necessary for answering complex mathematical problems and differential equations. In this paper, a detailed study on the use and concept of derivative that how it comes into existence, how it can be used to calculate the differential coefficients of a function at a particular point in an effective manner, and what are the applications of the rate of change of functions in mathematics as well as in real-life situations is presented. This study will help to understand the in-depth concept of calculus to the new researchers and students of mathematics.