AP Calculus BC Unit 3 practice questions: Differentiation: Composite, Implicit, and Inverse Functions
8 original multiple-choice questions on AP Calc BC Unit 3, differentiation: composite, implicit, and inverse functions. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
What is d/dx of arctan x?
Question 2 of 8
f is differentiable and one-to-one, with f(2) = 5 and f′(2) = 3. What is (f⁻¹)′(5)?
Question 3 of 8
For x² + y² = 25, what is dy/dx at the point (3, 4)?
Question 4 of 8
What is d/dx of sin(x²)?
Question 5 of 8
What is d/dx of e^(3x)?
Question 6 of 8
What is d/dx of ln(x² + 1)?
Question 7 of 8
What is d/dx of arcsin x?
Question 8 of 8
What is the second derivative of f(x) = sin x?
Key ideas in Unit 3
- The chain rule: d/dx f(g(x)) = f′(g(x))·g′(x). Most composite derivatives on the exam test it.
- Implicit differentiation: differentiate both sides with respect to x, treating y as a function of x, then solve for dy/dx.
- The derivative of an inverse function is (f⁻¹)′(b) = 1/f′(a) where f(a) = b.
- Memorize the inverse trig derivatives: arcsin, arccos and arctan.
- Higher-order derivatives are found by differentiating again; f″ describes concavity and acceleration.
More AP Calc BC practice
← Unit 2: Differentiation: Definition and Fundamental Properties
Unit 4: Contextual Applications of Differentiation →
The full AP Calculus BC practice test, all units
Studying from your own notes? Turn them into a practice quiz, a study guide or flashcards.