The document introduces key concepts of derivatives including: the definition of a derivative of a function f at a number a as the limit of the difference quotient as h approaches 0; that the derivative f'(a) represents the slope of the tangent line to the function f(x) at the point (a, f(a)); and that the derivative f'(a) represents the instantaneous rate of change of the function f(x) with respect to x when x equals a. It also briefly mentions differentiation as the process of calculating a derivative and the derivative theorem stating that if a function f is differentiable at a point a, then f must be continuous at a.