Question 3(a) Achieved

A product with sec, three readings off a drawn graph (continuity, stationary points, a limit), stationary points of a rational function, a related-rates cone, and an optimisation that has to be proved to a given exact value.

Differentiate y = √x sec(6x). You do not need to simplify your answer.

The 2024 paper, page 10 ↗ Marking schedule, page 5 ↗

Work it out

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

1. 1 Write the root as a power. What joins the two factors?

   y = x^1/2 sec 6x: a product.

2. 2 Differentiate each factor. What does the chain rule add to sec 6x?

   u = x^1/2, u' = (1/2) x^−1/2
   v = sec 6x, v' = 6 sec 6x tan 6x

3. 3 Put them together with the product rule.

   dy/dx = (1/2) x^−1/2 sec 6x + 6x^1/2 sec 6x tan 6x

What the marker wanted

• Achieved The correct derivative, in any equivalent form.

In our words, from NZQA’s 2024 marking schedule.

How did it go?

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