Year 12/AS Pure Chapter 12.1 (Differentiation)

An introduction to differentiation from first principles.

Hyperlinks to sections of this video:
Introduction: 00:00

Solution to Warm-Up Q1: 1:18
Solution to Warm-Up Q2: 2:51
Solution to Warm-Up Q3: 5:26
Solution to Warm-Up Q4: 6:17

Picture representations of tangents: 8:07
Definition(s) of a tangent to a curve: 8:48
Manually using the tangent to estimate the gradient: 9:48
Formal introduction to the tangent as a limit; gradient of y = x²: 14:11
Formal definition of the gradient function (dy/dx) : 20:12

Worked Example 1: Gradient from first principles for y=5x: 21:22
Worked Example 2: Gradient from first principles for y=3x²: 24:09
Worked Example 3: Gradient from first principles for y=x³: 27:22

Suggested exercises: 31:31

[MrBaileyMaths]

Links to video sections for tablets/smartphones:


Solution to Warm-Up Q1: 1:18
Solution to Warm-Up Q2: 2:51
Solution to Warm-Up Q3: 5:26
Solution to Warm-Up Q4: 6:17
Picture representations of tangents: 8:07
Definition(s) of a tangent to a curve: 8:48
Manually using the tangent to estimate the gradient: 9:48
Formal introduction to the tangent as a limit; gradient of y = x²: 14:11
Formal definition of the gradient function (dy/dx) : 20:12
Worked Example 1: Gradient from first principles for y=5x: 21:22
Worked Example 2: Gradient from first principles for y=3x²: 24:09
Worked Example 3: Gradient from first principles for y=x³: 27:22
Suggested exercises from textbook: 31:31