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Limits

Limits by direct substitutionLimits by factoring (0/0 forms)Limits at infinityOne-sided limits and continuity

Derivatives

Derivatives with the power ruleThe product and quotient rulesThe chain ruleDerivatives of trigonometric, exponential and logarithmic functionsEquations of tangent lines

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Critical points, extrema and increasing intervalsPosition, velocity and accelerationOptimization problemsRelated ratesConcavity and inflection points

Integrals

Indefinite integrals (antiderivatives)Definite integralsIntegration by substitutionArea between curvesRiemann sums and the trapezoidal rule

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Differential equations: initial value problemsExponential growth and decay models (dy/dt = ky)

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1. The product and quotient rules

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Difficulty

Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

The product and quotient rules practice

The product and quotient rules · 1–12

Find the derivative. Simplify.

Medium

1.f(x) = (6x + 5)(−6x² − 3x − 6)f′(x) =

Medium

2.f(x) = (−6x − 5)(6x² − x − 7)f′(x) =

Medium

3.f(x) = (3x + 1)(−2x² − 3)f′(x) =

Medium

4.f(x) = (−4x − 1)(2x² − 8x + 2)f′(x) =

Medium

5.f(x) = (−6x − 5)(−2x² − 7x + 8)f′(x) =

Medium

6.f(x) = (−5x + 2)(−4x² − 7x − 3)f′(x) =

Medium

7.f(x) = (3x + 4)(−4x² + 6)f′(x) =

Medium

8.f(x) = (2x + 3)(−3x² + 2x + 3)f′(x) =

Medium

9.f(x) = −x(−3x² − 8x + 8)f′(x) =

Medium

10.f(x) = (2x − 5)(3x² − x + 1)f′(x) =

Medium

11.f(x) = (6x − 8)(−2x² − 3x + 7)f′(x) =

Medium

12.f(x) = (5x − 2)(−4x² − 3x + 6)f′(x) =

Answer key — The product and quotient rules practice

The product and quotient rules

1.−108x² − 96x − 51

2.−108x² − 48x + 47

3.−18x² − 4x − 9

4.−24x² + 60x

5.36x² + 104x − 13

6.60x² + 54x + 1

7.−36x² − 32x + 18

8.−18x² − 10x + 12

9.9x² + 16x − 8

10.18x² − 34x + 7

11.−36x² − 4x + 66

12.−60x² − 14x + 36

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