Level 3 Differentiation Walkthrough

2020 NCEA Level 3 Differentiation Question 2(c)

2020 Paper

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Question

Scanned exam prompt asking for the stationary points of a function using product and chain rules.

First walkthrough idea

Focus to try first

Product and chain rules for stationary points.

Step 1

Apply the product rule

Differentiate with the product rule.

Show the first step’s working
\[ f(x)=(2x-3)e^{x^2+k} \] \[ f'(x) = 2e^{x^2+k} + (2x-3)e^{x^2+k}\cdot 2x \] \[ f'(x)=e^{x^2+k}(4x^2-6x+2) \]

Walkthrough overview

What this question practises

This 2020 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Product and chain rules for stationary points.

This is Question 2(c) from the 2020 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 and chain rules for stationary points. 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 2(b) Question 2(d) →