Exam Strategy

Calculus BC · AP · Differentiation — Definition and Fundamental Properties

CED focus

The Product Rule

This topic is assessed on the AP Exam.

Multiple-choice tips

• Identify whether the stem tests a definition, rule, or application.
• Separate average rate vs instantaneous rate in the stem.
• Eliminate derivative rules misapplied to products/quotients.
• Check units on rate answers in context MC.
• Use difference quotient structure when a definition is tested.

Free-response tips

• Label f′(a) meaning in context; show the rule that justifies each step.
• Show the limit definition when asked, then connect to a shortcut rule.
• Label what f′(a) means in context (velocity, marginal cost, slope).
• Show each differentiation rule step; do not skip the chain rule inner derivative.
• State units on derivative answers in applied FRQs.

Common traps

• Mixing average rate over an interval with instantaneous rate at a point
• Confusing average and instantaneous rate
• Forgetting +C only when it is an indefinite integral (not here)
• Applying the power rule to a product without product rule

Quick checklist

• [ ] Can state the derivative as a limit in words
• [ ] Can compute f′(a) with correct notation
• [ ] Can interpret a derivative in context with units