Level 3 Differentiation Walkthrough
2022 NCEA Level 3 Differentiation Question 1(a)
2022 Paper — Differentiation
Question
First walkthrough idea
Tip to try first
Think about the outside function and the inside function in \(y=(\ln x)^2\).
Step 1
Identify the differentiation rule
Reveal the explanation and working for this step.
Show the first step’s working
Recognise the composite-function structure before applying the chain rule.
Key result
This is a function inside a function, so we use the chain rule.
Walkthrough overview
What this question practises
This 2022 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Differentiation of the function.
This is Question 1(a) from the 2022 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.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise differentiation of the function. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.