Mathematics Advanced Year 11 - Module 3 - Lesson 5

The Chain Rule

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name

Date

Class

1. Key Ideas

What do a clock pendulum, a satellite orbiting Earth, and a sound wave all have in common? Their behaviour is described by functions inside functions. The chain rule is the key to differentiating these composite functions — and it is one of the most important tools in all of calculus.

The chain rule formula in both function and Leibniz notation
Why the derivative of a composite function involves multiplication of derivatives

2. Success Criteria

By the end, you should be able to:

The chain rule formula in both function and Leibniz notation
How to identify the "outer" and "inner" functions
That composite functions require the chain rule

3. Key Terms

DerivativeThe rate of change of a function at a point; the gradient of the tangent.

DifferentiationThe process of finding the derivative of a function.

Stationary PointA point where the derivative equals zero.

Chain RuleA rule for differentiating composite functions: dy/dx = dy/du × du/dx.

Product RuleA rule for differentiating products: d(uv)/dx = u(dv/dx) + v(du/dx).

Chain RuleFor composite functions: dy/dx = dy/du * du/dx.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

Prompt	Your answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The chain rule formula in both function and Leibniz notation". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "How to identify the "outer" and "inner" functions". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding The Chain Rule: "That composite functions require the chain rule".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about The Chain Rule but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about The Chain Rule?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of The Chain Rule?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The chain rule formula in both function and Leibniz notation