Course: Year 12 Mathematics Advanced

Differentiation Techniques

A HSC-focused unit for standard derivatives, chain rule, product rule, quotient rule, and applications to gradients, rates and stationary points.

Active lessons

5

Planned lessons

5

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Start with standard derivatives before rule combinations.
  • Use mastery quizzes to check rule selection under pressure.
  • Review earlier calculus lessons if tangent or stationary point setup feels rusty.
  • Work through the exam practice after chain, product and quotient rules.

What this unit covers

Standard trig, exponential and logarithmic derivatives
Chain rule
Product rule
Quotient rule
Tangents and normals
Rates and stationary point applications

Unit pathway

Lesson pathway

5 of 5 active

1

Lesson 1

Standard Derivatives: Trig, Exponential and Logarithmic Functions

Use standard derivatives of trigonometric, exponential and logarithmic functions, including simple linear combinations and numeric evaluations.

Active
2

Lesson 2

The Chain Rule

Differentiate composite functions using the chain rule, including powers, trigonometric, exponential and logarithmic composites.

Active
3

Lesson 3

Product and Quotient Rules

Use product and quotient rules with standard derivatives, while avoiding unnecessary symbolic simplification.

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4

Lesson 4

Applications with Extended Differentiation

Apply extended differentiation techniques to tangents, normals, rates of change and stationary point questions.

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5