Level 3 Differentiation Walkthrough

2022 NCEA Level 3 Differentiation Question 2(a)

2022 Paper - Product rule with trig chain rule

← Back to paper

Question

\[ \text{Differentiate } f(x)=(5x-3)\sin(4x). \]

You do not need to simplify your answer.

A later walkthrough visual becomes available with JavaScript; the complete question and first learning steps remain below.

First walkthrough idea

Tip to try first

Because the function is a product of two factors, start with the product rule.

Step 1

Identify the differentiation technique

Reveal the explanation and working for this step.

Show the first step’s working

Use the product rule because the function is a product of two factors.

Key result

Product rule

This is a product of two functions, so the product rule is the main technique.

Walkthrough overview

What this question practises

This 2022 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Product rule with a trig chain rule.

This is Question 2(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 product rule with a trig 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(e) Question 2(b) →