AP Calculus AB: Chain Rule — Drill 1

About This Drill

AP Calculus AB: Chain Rule — Drill 1 is a Math practice drill covering Chain Rule. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice applying the chain rule to differentiate composite functions involving polynomial, trigonometric, exponential, and logarithmic expressions. Questions target the most common chain rule errors, including forgetting the inner derivative and misidentifying the inside function.

Questions in This Drill

1. Let \( f(x) = (3x^2 + 1)^5 \). Find \( f'(x) \).
2. Let \( g(x) = \sin(4x^3) \). Find \( g'(x) \).
3. Let \( h(x) = e^{\sin x} \). Find \( h'(x) \).
4. Which of the following is the derivative of \( y = \ln(\cos x) \)?
5. Let \( f(x) = \sin^3(2x) \). Which of the following equals \( f'(x) \)?