← Differentiation methods: past papers
AS 91578 · 2025 paper · derivatives, normal, tangents
Question 1(a) Achieved
Practises The rules & standard derivatives
A chain-rule power, an oven cooling written in half-powers of t, a trig normal, a tangent to an exponential-plus-quadratic, and a parametric curve where inflection and stationary have to coincide.
Differentiate f(x) = (5x3 − 2x + 1)5. You do not need to simplify your answer.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 What is the outside function, and what is inside it?
A bracket raised to the fifth power. The outside is u5; the inside is u = 5x3 − 2x + 1. -
2 Chain rule: differentiate the outside, keep the inside, then multiply by the derivative of the inside.
f'(x) = 5(5x3 − 2x + 1)4 × (15x2 − 2)
What the marker wanted
- Achieved The correct derivative. It does not have to be simplified.
In our words, from NZQA’s 2025 marking schedule.
✕Common mistake
Expanding or tidying the derivative when the question says you need not. NZQA’s 2025 report says many students kept doing this, slipped while doing it, and lost a grade they had already earned, especially on the Achieved parts.How did it go?
Got it moves it further out. Review brings it back tomorrow.