Introduction to Differentiation
Rates of change, first principles, polynomial derivatives, tangents, normals, and applications.
Active lessons
11
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
11 of 11 active
Lesson 1
Rates of Change and Gradients
Practise rates of change and gradients with concise examples and mastery checks.
Lesson 2
Derivatives from First Principles
Practise derivatives from first principles with concise examples and mastery checks.
Lesson 3
Differentiating Polynomial Functions
Practise differentiating polynomial functions with concise examples and mastery checks.
Lesson 4
The Product Rule
Differentiate products of two functions using d/dx(uv) = u'v + uv'; identify when the product rule is needed versus expanding first.
Lesson 5
The Quotient Rule
Differentiate quotients using d/dx(u/v) = (u'v − uv')/v²; evaluate rational-function derivatives at given x-values.
Lesson 6
The Chain Rule
Differentiate composite polynomial functions of the form (ax+b)^n and (ax²+bx+c)^n using the chain rule.
Lesson 7
Stationary Points and the First Derivative Test
Find and classify stationary points of polynomial functions and determine intervals of increase and decrease.
Lesson 8
Second Derivative and Concavity
Find the second derivative, determine concavity, locate and confirm points of inflection, and apply the second derivative test.
Lesson 9
Tangents, Normals and Applications
Practise tangents, normals and applications with concise examples and mastery checks.
Lesson 10
Curve Sketching Using Calculus
Combine intercepts, stationary points, increasing/decreasing intervals, concavity, and inflection points to describe a curve using calculus.
Lesson 11
Introduction to Differentiation Exam Practice
Practise introduction to differentiation exam practice with concise examples and mastery checks.
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