The chain rule cracks open every composite function. Implicit differentiation finds a slope on curves you can’t even solve for. Inverses turn a derivative on its head. Five interactive lessons that make the course’s trickiest differentiation techniques into things you can watch unfold — built straight on the rules from Unit 2.
Work them in order for a full walkthrough of the unit, or jump straight to whatever's giving you trouble.
The master key of Unit 3. To differentiate a composite f(g(x)), peel it one layer at a time — the derivative of the outer (left alone on the inner) times the derivative of the inner. Spot the inner and outer functions, then chain. Almost everything else in the unit leans on it.
When y is tangled up with x and won’t come loose, you differentiate anyway. Treat y as a function of x, apply the chain rule to every y-term, then solve for dy/dx. Suddenly you can find the slope on a circle, an ellipse, or a curve that isn’t a function at all.
Reflect a function across y = x and its slope flips to a reciprocal: (f⁻¹)′ = 1 / f′ at the matching point. That one idea unlocks the derivatives of arcsin, arccos, and arctan — the pieces you’ll lean on for the rest of the course.
Differentiate, then do it again. The second derivative measures how the rate itself changes — concavity, acceleration — and the notation d²y/dx² has its own logic. The third, fourth, and beyond follow the same move, often with patterns that repeat.
The synthesis lesson. Faced with a messy function, which rule fires first — power, product, quotient, chain, or implicit? Learn to read a function’s structure from the outside in and pick the most efficient path, spiraling together everything from Units 2 and 3.
Put it together the way the real AP exam does — mixed multiple choice first, then full free-response — with a one-page formula sheet to review from.
Thirty multiple-choice questions across all five lessons — the chain rule, implicit differentiation, inverse and inverse-trig derivatives, higher-order derivatives, and selecting procedures — pulled in fresh batches with worked explanations that name every distractor’s mistake, plus chained free-response problems in the classic AP Section II mold with typed answers graded against the rubric.
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