Inverse trigonometric functions — Arccos chain

Question

Differentiate .

This practice question was inspired by Question 11(e) in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: use the restricted domain and range that make the inverse function single-valued. with , .
State the final answer clearly in the form the question requested.Answer: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Sign is negative for arccos.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.