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AP Calculus BC 2.9 Quotient Rule Overview

Apply the quotient rule to rational and graph-defined functions, combine it with other rules and evaluate derivatives at specified points.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • differentiate parametric or polar equations and interpret the result
  • apply the appropriate derivative or area integral in context

Covered syllabus points

FUN-3.B—Calculate derivatives of products and quotients of differentiable functions—Topic 2.9

2.9 The Quotient Rule question 1

[Maximum number: 1]

If y=x3x+2y=\frac{x^{3}}{x+2}, then dydx=\frac{d y}{d x}=

A

3x23 x^{2}

B

−2x3−6x2(x+2)2\frac{-2 x^{3}-6 x^{2}}{(x+2)^{2}}

C

2x3+6x2(x+2)2\frac{2 x^{3}+6 x^{2}}{(x+2)^{2}}

D

4x3+6x2(x+2)2\frac{4 x^{3}+6 x^{2}}{(x+2)^{2}}

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