The derivative arrives. Define it as the limit of average rates of change, connect it to the slope of the tangent line and to continuity, then learn the fundamental rules — power, product, and quotient — and the derivatives of the key functions.
Six ways to master Unit 2 — pick whichever fits how you like to study.
All 10 topics from the College Board CED, in order.
Unit 2 introduces the derivative, the second central idea of calculus. It grows from Unit 1's limits: the average rate of change over an interval is the slope of a secant line, and the instantaneous rate of change is the limit of those averages as the interval shrinks — which is the derivative. Formally, f′(x) = lim(h→0) [f(x+h) − f(x)]/h, and it equals the slope of the tangent line to the graph.
You'll connect differentiability and continuity (differentiable functions are continuous, but not the reverse — think of a corner), and see where derivatives fail to exist. Then the unit builds your toolkit of fundamental rules: the power rule, the constant/sum/difference/constant-multiple rules, the derivatives of sin x, cos x, eᵇ, and ln x, and the product and quotient rules — finishing with the derivatives of the remaining trigonometric functions.
On the exam this unit is 10–12% for AB and 4–7% for BC, and takes about 13 class periods (AB). The four mathematical practices below run through every topic: