Derivative as a Function (f') - Expii

If f(x) is differentiable at many points (typically, everywhere or on an interval), we can "collect derivatives" into a derivative function f'(x). This function gives the changing slope of the function y=f(x). The derivative function also gives the instantaneous rate of change at specific points of the function. Derivative functions appear in higher derivatives, the graphical analysis of curves, and the Fundamental Theorem of Calculus (FTC).