Level 3 Differentiation Walkthrough

2024 NCEA Level 3 Differentiation Question 1(a)

2024 Paper

← Back to paper

Question

\[ \text{Differentiate } f(x)=\sqrt{4-9x^4}. \]

You do not need to simplify your answer.

First walkthrough idea

Hint to try first

Taking the square root is the same as raising the bracket to the power of \(\frac{1}{2}\).

Step 1

Rewrite the square root first

Writing the square root as a power of \(\frac{1}{2}\) makes the chain rule much easier to see.

Show the first step’s working

Writing the square root as a power of \(\frac{1}{2}\) makes the chain rule much easier to see.

Key result

\[ \left(4 - 9 x^{4}\right)^{\left(\frac{1}{2}\right)} \]

Walkthrough overview

What this question practises

This 2024 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Rewriting a square root as a power and applying the chain rule.

This is Question 1(a) from the 2024 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 rewriting a square root as a power and applying the chain rule. 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) →