Level 3 Differentiation Walkthrough

2023 NCEA Level 3 Differentiation Question 3(a)

2023 Paper

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Question

\[ \text{Differentiate } y=\ln(x^2-x^4+1). \]

You do not need to simplify your answer.

First walkthrough idea

Hint to try first

For \(y=\ln(u)\), the derivative is \(\frac{u'}{u}\).

Step 1

Differentiate the inside first

Differentiate term by term before using the logarithm rule.

Show the first step’s working

Differentiate term by term before using the logarithm rule.

Key result

\[ 2x-4x^3 \]

Walkthrough overview

What this question practises

This 2023 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: The chain rule inside a logarithm.

This is Question 3(a) from the 2023 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 the chain rule inside a logarithm. 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 2(e) Question 3(b) →