AP Calculus AB: Derivatives of Inverse and Inverse Trig Functions — Drill 1

About This Drill

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

Practice differentiating inverse functions using the inverse function derivative formula and find derivatives of arcsin, arccos, and arctan. These AP Calculus AB techniques appear regularly on the multiple-choice and free-response sections.

Questions in This Drill

1. If \( \dfrac{d}{dx}[\arctan x] = \dfrac{1}{1+x^2} \), what is \( \dfrac{d}{dx}[\arctan(3x)] \)?
2. What is \( \dfrac{d}{dx}[\arcsin x] \)?
3. Let \( f \) be a differentiable function with \( f(2) = 5 \) and \( f'(2) = 4 \). If \( g = f^{-1} \), what is \( g'(5) \)?
4. The function \( f(x) = x^3 + x \) is one-to-one for all real \( x \). If \( g = f^{-1} \), what is \( g'(2) \)?
5. Let \( h(x) = \arcsin(x^2) \). Which of the following correctly gives \( h'(x) \) and identifies a value of \( x \) where \( h'(x) \) does not exist?