Level 3 Differentiation Walkthrough

2017 NCEA Level 3 Differentiation Question 2(a)

2017 Paper

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Question

\[\text{Differentiate }y=2(x^2-4x)^5.\]

You do not need to simplify your answer.

First walkthrough idea

Focus to try first

Keep the nested power intact: differentiate the outside first, then multiply by the derivative of the inside.

Step 1

Identify the inner and outer functions

A substitution can make the two layers of the composite function easier to see.

Show the first step’s working
\[u=x^2-4x,\qquad y=2u^5\]

Walkthrough overview

What this question practises

This 2017 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Chain rule differentiation of a composite fifth power.

This is Question 2(a) from the 2017 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 composite 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(e) Question 2(b) →