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Unit test: 20 questions, easy to hard, 2 points each, roomy spacing. Keeps your selected skills.

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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

Applications of derivatives

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) = 2x(x² + 4)f′(x) =

Medium

2.f(x) = (−6x − 3)(4x² + x − 1)f′(x) =

Medium

3.f(x) = 3x(5x² + 5x + 9)f′(x) =

Medium

4.f(x) = x(5x² − 6x − 3)f′(x) =

Medium

5.f(x) = (−5x + 9)(4x² − 9x + 4)f′(x) =

Medium

6.f(x) = −5x(−x² − 7x + 3)f′(x) =

Medium

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

Medium

8.f(x) = (−3x + 7)(x² + x + 8)f′(x) =

Medium

9.f(x) = (−3x − 1)(3x² − 8x − 8)f′(x) =

Medium

10.f(x) = −4x(6x² − 2x + 2)f′(x) =

Medium

11.f(x) = (5x + 5)(2x² + 2)f′(x) =

Medium

12.f(x) = (−x + 9)(−3x² − 2x + 6)f′(x) =

Answer key — The product and quotient rules practice

The product and quotient rules

1.6x² + 8

2.−72x² − 36x + 3

3.45x² + 30x + 27

4.15x² − 12x − 3

5.−60x² + 162x − 101

6.15x² + 70x − 15

7.−48x² − 56x − 28

8.−9x² + 8x − 17

9.−27x² + 42x + 32

10.−72x² + 16x − 8

11.30x² + 20x + 10

12.9x² − 50x − 24

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