Level 3 Differentiation Walkthrough

2024 NCEA Level 3 Differentiation Question 1(b)

2024 Paper

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Question

A curve is defined by the equation \[ y=(x^2+3x+2)\sin x. \]

Find the gradient of the tangent to this curve when \(x=0\).

You must use calculus and show any derivatives that you need to find when solving this problem.

First walkthrough idea

Hint to try first

Here we have two functions multiplied together, so start with the product rule.

Step 1

Identify the main rule

The function is one factor times another, so the product rule is the obvious starting point.

Show the first step’s working

The function is one factor times another, so the product rule is the obvious starting point.

Key result

Product rule

Walkthrough overview

What this question practises

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

Method: Product rule differentiation and evaluating the gradient at \(x=0\).

This is Question 1(b) 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.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise product rule differentiation and evaluating the gradient at \(x=0\). Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Differentiate both factors in turn and keep both product-rule terms.

Continue practising

← Question 1(a) Question 1(c) →