Free Grade 3 Introducing Chain Rule Worksheets
Free Grade 3 worksheets for Introducing Chain Rule: 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing chain rule
Explain introducing chain rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing chain rule
Calculate introducing chain rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing chain rule
Compare introducing chain rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing chain rule
Justify introducing chain rule 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 Introducing Chain Rule 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 = 6x^3 + 5x.[1]
- 2.Differentiate y = 4x^5 + 9x.[1]
- 3.Differentiate y = 1x^4 + 4x.[1]
- 4.Differentiate y = 2x^4 + 7x.[1]
- 5.Differentiate y = 3x^5 + 1x.[2]
- 6.Differentiate y = 4x^5 + 6x.[2]
- 7.Differentiate y = 6x^2 + 3x.[2]
- 8.Differentiate y = 6x^3 + 7x.[2]
- 9.Find the gradient of y = 4x^3 + 5x at x = 2.[3]
- 10.Find the gradient of y = 2x^2 + 9x at x = 2.[3]
- 11.Find the gradient of y = 5x^3 + 9x at x = 3.[3]
- 12.Find the gradient of y = 3x^5 + 6x at x = 3.[3]
Show answers and working
1. dy/dx = 18x^2 + 5
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 5x → 5.
2. dy/dx = 20x^4 + 9
Multiply by the power, then reduce the power by 1. 4x^5 → 20x^4; 9x → 9.
3. dy/dx = 4x^3 + 4
Multiply by the power, then reduce the power by 1. 1x^4 → 4x^3; 4x → 4.
4. dy/dx = 8x^3 + 7
Multiply by the power, then reduce the power by 1. 2x^4 → 8x^3; 7x → 7.
5. dy/dx = 15x^4 + 1
Multiply by the power, then reduce the power by 1. 3x^5 → 15x^4; 1x → 1.
6. dy/dx = 20x^4 + 6
Multiply by the power, then reduce the power by 1. 4x^5 → 20x^4; 6x → 6.
7. dy/dx = 12x^1 + 3
Multiply by the power, then reduce the power by 1. 6x^2 → 12x^1; 3x → 3.
8. dy/dx = 18x^2 + 7
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 7x → 7.
9. 53
dy/dx = 12x^2 + 5. At x = 2: 12 × 4 + 5 = 53.
10. 17
dy/dx = 4x^1 + 9. At x = 2: 4 × 2 + 9 = 17.
11. 144
dy/dx = 15x^2 + 9. At x = 3: 15 × 9 + 9 = 144.
12. 1221
dy/dx = 15x^4 + 6. At x = 3: 15 × 81 + 6 = 1221.
Worked examples
Differentiate y = 4x^3 + 8x.
- Multiply by the power, then reduce the power by 1.
- 4x^3 → 12x^2; 8x → 8.
- Answer: dy/dx = 12x^2 + 8
Differentiate y = 4x^5 + 3x.
- Multiply by the power, then reduce the power by 1.
- 4x^5 → 20x^4; 3x → 3.
- Answer: dy/dx = 20x^4 + 3
Find the gradient of y = 2x^3 + 9x at x = 1.
- dy/dx = 6x^2 + 9.
- At x = 1: 6 × 1 + 9 = 15.
- Answer: 15
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 Introducing Chain Rule 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 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 Introducing Chain Rule?
- Move on to Working with Chain Rule, Chain Rule in Context, Rate of Change, Differentiating Powers, which build directly on this idea.
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