A function which calculates the slope of a curve; that is, the slope of the tangent line to the graph of the function at that point. The derivative of a function f at a point x is commonly written f '(x). For example, if f(x) = x³ then f '(x) = 3x². The slope of the tangent line when x = 5 is f '(x) = 3·5² = 75.