Level 3 Differentiation Walkthrough
2016 NCEA Level 3 Differentiation Question 1(a)
2016 Paper
Question
First walkthrough idea
Focus to try first
Rewrite each reciprocal as a negative power, then apply the power rule term by term.
Step 1
Rewrite the reciprocal terms
Negative powers make the power rule visible.
Show the first step’s working
The function is defined for \(x\ne0\), so its derivative will have the same restriction.
Walkthrough overview
What this question practises
This 2016 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.
Method: Power rule differentiation with negative exponents.
This is Question 1(a) from the 2016 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.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise power rule differentiation with negative exponents. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.