2024 HSC Mathematics Extension 1
Question 11(e):
Inverse trigonometric functions
Differentiate the function .
How to recognise this question
Question type: inverse trigonometric functions
- The command and notation point to inverse trigonometric functions.
- The requested response is a short answer.
How to handle it: use the restricted domain and range that make the inverse function single-valued.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Chain rule: if with , then .
- Here and .
- Hence .
- NESA 11(e): 1 mark for the correct derivative.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Differentiate .
Question 2
Differentiate .
Question 3
Find if .