Unit 2 · Differentiation: Definition and Fundamental Properties

Chapter 2.2

When Derivatives Exist — and When They Don't

Continuity was about not breaking; differentiability is about not bending sharply. Corners, cusps, and vertical tangents.

10–14 min · free · lesson 10 of 46

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By the end

  1. 01Estimate derivatives from tables and graphs
  2. 02Explain why differentiability implies continuity and why the converse fails
  3. 03Identify points where a function is not differentiable

In unit 2

  1. 2.1Defining the Derivative12–16
  2. 2.2When Derivatives Exist — and When They Don't10–14
  3. 2.3The First Derivative Rules10–14
  4. 2.4The Derivatives Nature Chose: sin, cos, eˣ, ln11–15
  5. 2.5Products, Quotients, and the Rest of Trig12–16
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