Level 3 Differentiation Walkthrough

2018 NCEA Level 3 Differentiation Question 1(a)

2018 Paper

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Question

\[ \text{Differentiate }y=2x^3+\frac{5}{(x^3+2)^3}. \]

You do not need to simplify your answer.

First walkthrough idea

Focus to try first

Rewrite the fraction with a negative power, then use the power rule and chain rule.

Step 1

Rewrite the fraction

A denominator power can be written as a negative exponent.

Show the first step’s working
\[y=2x^3+5(x^3+2)^{-3}\]

Walkthrough overview

What this question practises

This 2018 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Negative powers with the power and chain rules.

This is Question 1(a) from the 2018 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 negative powers with the power and 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) →