In mathematics (particularly in differential calculus), the derivative is a way to show the instantaneous rate of change: that is, the amount by which a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph. The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) for a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object for time is the object's velocity: this measures how quickly the position of the object changes when time advances.