Free Grade 3 Chain Rule in Context Worksheets
Free Grade 3 worksheets for Chain Rule in Context: 12 real questions with a full answer key and worked solutions. Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
Free
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify chain rule in context
Identify chain rule in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain chain rule in context
Explain chain rule in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate chain rule in context
Calculate chain rule in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare chain rule in context
Compare chain rule in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Chain Rule in Context works
Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Differentiate y = 2x^3 + 2x.[1]
- 2.Differentiate y = 6x^5 + 3x.[1]
- 3.Differentiate y = 4x^4 + 1x.[1]
- 4.Differentiate y = 6x^4 + 8x.[1]
- 5.Differentiate y = 6x^2 + 8x.[2]
- 6.Differentiate y = 2x^4 + 8x.[2]
- 7.Differentiate y = 3x^3 + 8x.[2]
- 8.Differentiate y = 5x^5 + 3x.[2]
- 9.Find the gradient of y = 1x^2 + 7x at x = 1.[3]
- 10.Find the gradient of y = 4x^5 + 7x at x = 2.[3]
- 11.Find the gradient of y = 5x^5 + 5x at x = 3.[3]
- 12.Find the gradient of y = 6x^2 + 5x at x = 1.[3]
Show answers and working
1. dy/dx = 6x^2 + 2
Multiply by the power, then reduce the power by 1. 2x^3 → 6x^2; 2x → 2.
2. dy/dx = 30x^4 + 3
Multiply by the power, then reduce the power by 1. 6x^5 → 30x^4; 3x → 3.
3. dy/dx = 16x^3 + 1
Multiply by the power, then reduce the power by 1. 4x^4 → 16x^3; 1x → 1.
4. dy/dx = 24x^3 + 8
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 8x → 8.
5. dy/dx = 12x^1 + 8
Multiply by the power, then reduce the power by 1. 6x^2 → 12x^1; 8x → 8.
6. dy/dx = 8x^3 + 8
Multiply by the power, then reduce the power by 1. 2x^4 → 8x^3; 8x → 8.
7. dy/dx = 9x^2 + 8
Multiply by the power, then reduce the power by 1. 3x^3 → 9x^2; 8x → 8.
8. dy/dx = 25x^4 + 3
Multiply by the power, then reduce the power by 1. 5x^5 → 25x^4; 3x → 3.
9. 9
dy/dx = 2x^1 + 7. At x = 1: 2 × 1 + 7 = 9.
10. 327
dy/dx = 20x^4 + 7. At x = 2: 20 × 16 + 7 = 327.
11. 2030
dy/dx = 25x^4 + 5. At x = 3: 25 × 81 + 5 = 2030.
12. 17
dy/dx = 12x^1 + 5. At x = 1: 12 × 1 + 5 = 17.
Worked examples
Differentiate y = 4x^4 + 9x.
- Multiply by the power, then reduce the power by 1.
- 4x^4 → 16x^3; 9x → 9.
- Answer: dy/dx = 16x^3 + 9
Differentiate y = 5x^2 + 9x.
- Multiply by the power, then reduce the power by 1.
- 5x^2 → 10x^1; 9x → 9.
- Answer: dy/dx = 10x^1 + 9
Find the gradient of y = 3x^3 + 9x at x = 2.
- dy/dx = 9x^2 + 9.
- At x = 2: 9 × 4 + 9 = 45.
- Answer: 45
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Forgets that a constant differentiates to 0.
Correction: Constants have zero gradient.
Reduces the power but forgets to multiply by it.
Correction: Multiply by the power, then reduce it by 1.
Teacher tips
- · Link to gradients of straight lines first.
Parent tips
- · Ask how speed relates to distance over time.
Real-life applications
- · Speed from distance, maximising profit.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Chain Rule in Context worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Chain Rule, Introducing Chain Rule, Stationary Points. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Chain Rule in Context?
- Move on to Rate of Change, Differentiating Powers, Tangents and Normals, Stationary Points, which build directly on this idea.
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