Year 12/AS Pure Chapter 12.2 (Differentiation)

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Deriving some important results using differentiation from first principles, including the derivatives of xⁿ and axⁿ.

Hyperlinks to sections of this video:
Introduction: 00:00
Solution to Warm-Up Q1: 0:56
Solution to Warm-Up Q2: 2:52
Solution to Warm-Up Q3: 4:28
Solution to Warm-Up Q4: 7:38
Last lesson recap - can you spot the general pattern?: 9:07
Proving the derivative of y=xⁿ from first principles: 11:28
Proving the derivative of y=axⁿ from first principles: 17:56
Worked examples: differentiating functions of the type y=axⁿ: 24:15
Further worked examples : 26:06
Worked example - differentiating a quadratic: 29:39
Suggested exercises from textbook: 40:11
  1. Mr Bailey Maths
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Hyperlinks to video sections for tablets and smartphones:


Solution to Warm-Up Q1: 0:56
Solution to Warm-Up Q2: 2:52
Solution to Warm-Up Q3: 4:28
Solution to Warm-Up Q4: 7:38
Last lesson recap - can you spot the general pattern?: 9:07
Proving the derivative of y=xⁿ from first principles: 11:28
Proving the derivative of y=axⁿ from first principles: 17:56
Worked examples: differentiating functions of the type y=axⁿ: 24:15
Further worked examples : 26:06
Worked example - differentiating a quadratic: 29:39
Suggested exercises from textbook: 40:11

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