← Differentiation methods: past papers

AS 91578 · 2023 paper · gradient of normal, turning points, a proof

Question 3(a) Achieved

Practises The rules & standard derivatives

A log chain rule, three readings off a drawn graph, a parametric normal on a Ferris wheel, stationary points of a reciprocal pair, and a catenary to verify by substitution.

Differentiate y = ln(x2 − x4 + 1). You do not need to simplify your answer.

The 2023 paper, page 10 ↗ Marking schedule, page 6 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

  1. 1 How do you differentiate ln of a function?

    The derivative of the inside, over the inside.

  2. 2 Differentiate the inside and put it together.

    (d/dx)(x2 − x4 + 1) = 2x − 4x3, so dy/dx = (2x − 4x3)/(x2 − x4 + 1).
Answer dy/dx = (2x − 4x3)/(x2 − x4 + 1).

What the marker wanted

  • Achieved The correct derivative.

In our words, from NZQA’s 2023 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.