AP Calculus AB: Basic Differentiation Rules — Drill 1

About This Drill

AP Calculus AB: Basic Differentiation Rules — Drill 1 is a Math practice drill covering Basic Differentiation Rules. 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 power rule, constant rule, sum/difference rule, and derivatives of exponential, logarithmic, and trigonometric functions. These AP Calculus AB differentiation skills are essential for every subsequent unit.

Questions in This Drill

1. What is \( \dfrac{d}{dx}\left[4x^3 - 7x + 2\right] \)?
2. If \( f(x) = 3\sin x - 5\cos x \), then \( f'(x) = \)
3. If \( g(x) = \dfrac{6}{x^2} + 4\sqrt{x} \), then \( g'(x) = \)
4. Let \( h(x) = e^x + \ln x \). Which of the following correctly states \( h'(x) \) and evaluates \( h'(1) \)?
5. Let \( f(x) = 2\sin x + e^x - x^3 \). A student claims that \( f'(\pi) = e^\pi \) because "the derivative of \( \sin x \) is zero at \( x = \pi \) since \( \sin\pi = 0 \), and the derivative of \( x^3 \) is zero because \( \pi \) is just a constant being plugged in, so that term disappears." Which of the following is the correct value of \( f'(\pi) \)?