Derivative
![The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.](/Images/godic/202501/20/Tangent_to_a_curve.svg2621.png")
![Rate of change as a limit valueFigure 1. The tangent line at (x, f(x))Figure 2. The secant to curve y= f(x) determined by points (x, f(x)) and (x+h, f(x+h))Figure 3. The tangent line as limit of secantsFigure 4. Animated illustration: the tangent line (derivative) as the limit of secants](/Images/godic/202501/20/Tangent-calculus.svg2621.png")
![](/Images/godic/202501/20/Secant-calculus.svg2621.png")
![](/Images/godic/202501/20/Lim-secant.svg2621.png")
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced.