AP Calculus AB: Implicit Differentiation — Drill 1

About This Drill

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

Practice finding dy/dx for implicitly defined curves, including tangent line slopes and second derivatives using implicit differentiation. These AP Calculus AB skills appear on both the multiple-choice and free-response sections.

Questions in This Drill

1. If \( x^2 + y^2 = 25 \), what is \( \dfrac{dy}{dx} \)?
2. Find \( \dfrac{dy}{dx} \) if \( 3x^2 - 2y^3 = 7 \).
3. The curve \( x^2 + xy + y^2 = 7 \) passes through the point \( (1, 2) \). What is the slope of the tangent line at \( (1, 2) \)?
4. Suppose \( F(x, y) = 0 \) implicitly defines \( y \) as a function of \( x \) near a point where \( \dfrac{dy}{dx} \) exists. Which of the following statements is always true?
5. Given \( x^2 + y^2 = 25 \), find \( \dfrac{d^2y}{dx^2} \) in simplified form.