what is a derivative in math

In mathematics, a derivative is a measure of how much a function changes as its input changes. It shows the sensitivity of change of a functions output with respect to the input. The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point. The derivative is often described as the "instantaneous rate of change," which is the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. The derivative is primarily used when there is some varying quantity, and the rate of change of that quantity is to be determined. The derivative is a fundamental tool of calculus and is used in many areas of mathematics, science, and engineering.