Extend differentiation to the functions the basic rules can't reach. Master the chain rule for composites, implicit differentiation for equations not solved for y, the derivatives of inverse and inverse trig functions, and higher-order derivatives.
Six ways to master Unit 3 — pick whichever fits how you like to study.
All 6 topics from the College Board CED, in order.
Unit 3 extends differentiation to functions the basic rules of Unit 2 can't handle directly. The chain rule differentiates composite functions — d/dx[f(g(x))] = f′(g(x))·g′(x) — and it powers almost everything that follows. Implicit differentiation applies the chain rule to equations that aren't solved for y (like x² + y² = 25), differentiating both sides with respect to x and solving for dy/dx.
You'll then find derivatives of inverse functions using (f⁻¹)′(x) = 1/f′(f⁻¹(x)), including the inverse trigonometric functions arcsin, arccos, and arctan. Topic 3.5 is about selecting the right procedure — deciding which combination of rules a messy function needs — and Topic 3.6 introduces higher-order derivatives, found by differentiating repeatedly.
On the exam this unit is 9–13% for AB and 4–7% for BC, and takes about 13 class periods (AB). The four mathematical practices below run through every topic: