Level 3 Differentiation Walkthrough

2021 NCEA Level 3 Differentiation Question 1(a)

2021 Paper

← Back to paper

Question

\[ \text{Differentiate } y=e^{3x}\sin 2x. \]

You do not need to simplify your answer.

First walkthrough idea

Focus to try first

Treat \(e^{3x}\) and \(\sin 2x\) as two separate factors, then use the product rule.

Step 1

Name the two factors

The function is a product, so set up \(u\) and \(v\).

Show the first step’s working
\[ u=e^{3x},\qquad v=\sin 2x \]

Walkthrough overview

What this question practises

This 2021 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Product rule with exponential and trigonometric chain rules.

This is Question 1(a) from the 2021 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 exponential and trigonometric chain rules. 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) →