Exam Strategy

Calculus AB · AP · Differentiation — Composite, Implicit, and Inverse Functions

CED focus

Differentiating Inverse Functions

This topic is assessed on the AP Exam.

Multiple-choice tips

• Identify whether the stem tests a definition, rule, or application.
• Circle inner/outer functions before chain-rule MC.
• Eliminate implicit differentiation answers that treat y as constant.
• Check inverse-function derivative formulas for domain issues.
• On MC graphs, read whether the question asks for slope or value.

Free-response tips

• Label f′(a) meaning in context; show the rule that justifies each step.
• Show dy/dx setup clearly for implicit differentiation.
• Write the chain rule as a product of derivatives.
• Justify inverse derivative with f′(g(x))·g′(x) structure.
• Simplify only after showing the correct rule application.

Common traps

• Mixing average rate over an interval with instantaneous rate at a point
• Missing the inner derivative on composite functions
• Treating y as constant during implicit differentiation
• Using an inverse derivative without checking differentiability

Quick checklist

• [ ] Can apply the chain rule on a nested function
• [ ] Can differentiate implicitly for a simple relation
• [ ] Can name which rule justifies each step