NCEA maths skill practice
Chain Rule NCEA practice questions
Practise differentiating composite functions across powers, roots, logarithms, trigonometric functions, and exponential functions.
Skill overview
What these questions practise
The matched questions explicitly use the chain rule, sometimes after rewriting a root or negative power. They then apply the derivative to gradients, stationary points, rates, or second-derivative reasoning.
Relevant standards: NCEA Level 3 Differentiation — AS91578
This collection contains 30 matching walkthroughs across 10 examination years.
The grouping is based on the method recorded for each walkthrough. Use the linked NZQA standard and paper material for authoritative wording, diagrams, and assessment information.
Before you start
Common mistakes in these methods
- Differentiate the outer expression while retaining the inner expression, then multiply by the inner derivative.
- After rewriting a root or reciprocal as a power, keep the new exponent and any negative sign consistent through differentiation.
- For a trigonometric, logarithmic, or exponential composite, include the derivative of its complete inside expression.
Related practice
Chain Rule questions from different years
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30 matching questions shown.
NCEA Level 3 · AS91578 2025 Differentiation 1 question
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NCEA Level 3 · AS91578 2024 Differentiation 3 questions
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NCEA Level 3 · AS91578 2023 Differentiation 3 questions
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NCEA Level 3 · AS91578 2022 Differentiation 3 questions
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NCEA Level 3 · AS91578 2021 Differentiation 4 questions
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NCEA Level 3 · AS91578 2020 Differentiation 3 questions
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NCEA Level 3 · AS91578 2019 Differentiation 3 questions
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NCEA Level 3 · AS91578 2018 Differentiation 1 question
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NCEA Level 3 · AS91578 2017 Differentiation 4 questions
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NCEA Level 3 · AS91578 2016 Differentiation 5 questions
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