Level 3 Differentiation Walkthrough

2023 NCEA Level 3 Differentiation Question 2(b)

2023 Paper

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Question

Find the gradient of the tangent to the curve \(y=\cot(2x)\) at the point where

\[ x=\frac{\pi}{12}. \]

You must use calculus and show any derivatives that you need to find when solving this problem.

First walkthrough idea

Hint to try first

The derivative of \(\cot u\) is \(-\csc^2(u)\cdot u'\).

Step 1

Differentiate the curve

The chain rule adds the factor of \(2\) from differentiating \(2x\).

Show the first step’s working

The chain rule adds the factor of \(2\) from differentiating \(2x\).

Key result

\[ y'=-2\csc^2(2x) \]

Walkthrough overview

What this question practises

This 2023 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Chain rule differentiation of \(y=\cot(2x)\).

This is Question 2(b) from the 2023 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise chain rule differentiation of \(y=\cot(2x)\). Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Do not stop after differentiating the outside function; include the derivative of the inside function as a factor.

Continue practising

← Question 2(a) Question 2(c) →