In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity. Conversely, the integral of the object's velocity over time is how much the object's position changes from the time when the integral begins to the time when the integral ends.
