Chain Rule NCEA practice questions

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

Open a question for hints and a progressive worked solution, or use the standard and paper links to return to its assessment context.

Keep practising

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