👉 In mathematics, a derivative is a function that measures how much one quantity changes in relation to another. It is typically represented using an arrow pointing from the input variable to the output variable. Derivatives allow us to study relationships between quantities by analyzing their rates of change. In the context of calculus and mathematical models, derivatives are fundamental tools for understanding various phenomena such as growth, decay, rate of change, and optimization problems. They provide insights into the behavior of functions and help solve complex problems in