Level 3 Differentiation Walkthrough

2020 NCEA Level 3 Differentiation Question 1(a)

2020 Paper

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Question

Scanned exam prompt asking for the derivative of a fifth power using the chain rule.

First walkthrough idea

Focus to try first

Chain rule differentiation of a fifth power.

Step 1

Apply the chain rule

The fifth power is applied to a function of \(x\), so the chain rule connects the outer and inner derivatives.

Show the first step’s working

Use the chain rule because the fifth power is applied to a function of \(x\).

Walkthrough overview

What this question practises

This 2020 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Chain rule differentiation of a fifth power.

This is Question 1(a) from the 2020 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise chain rule differentiation of a fifth power. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Do not stop after differentiating the outside function; include the derivative of the inside function as a factor.

Continue practising

Question 1(b) →