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We pick the skills and settings; every question and answer is still computed, so the key stays correct.

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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

Differential equations

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

Each skill gets its own section. Up to 8 skills per sheet.

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Square roots

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Number optionsNo negative numbersWhole-number answers only (no fractions or decimals)

Largest number in a question

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Step-by-step answer keyPro: each answer shows its working in the PDF.QR code for the answersPrints a code that opens the answer key on a phone, so work can be checked at home.

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1. The chain rule

Questions

Difficulty

Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

The chain rule practice

The chain rule · 1–12

Find the derivative.

Hard

1.f(x) = √5x² + 7x + 3f′(x) =

Hard

2.f(x) = √6x² + 6x − 1f′(x) =

Hard

3.f(x) = √x² + 4x − 4f′(x) =

Hard

4.f(x) = √5x² + 6x + 9f′(x) =

Hard

5.f(x) = √3x² + 4f′(x) =

Hard

6.f(x) = √5x² − 7x + 3f′(x) =

Hard

7.f(x) = √2x² − 9x − 6f′(x) =

Hard

8.f(x) = √6x² − 9f′(x) =

Hard

9.f(x) = √6x² − x + 6f′(x) =

Hard

10.f(x) = √5x² + 6x − 7f′(x) =

Hard

11.f(x) = √4x² + 2x − 3f′(x) =

Hard

12.f(x) = √5x² + 7x + 8f′(x) =

Answer key — The chain rule practice

The chain rule

1.10x + 72√5x² + 7x + 3

2.12x + 62√6x² + 6x − 1

3.2x + 42√x² + 4x − 4

4.10x + 62√5x² + 6x + 9

5.6x2√3x² + 4

6.10x − 72√5x² − 7x + 3

7.4x − 92√2x² − 9x − 6

8.12x2√6x² − 9

9.12x − 12√6x² − x + 6

10.10x + 62√5x² + 6x − 7

11.8x + 22√4x² + 2x − 3

12.10x + 72√5x² + 7x + 8

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