Unit 2 · Differentiation: Definition and Fundamental Properties

Chapter 2.4

The Derivatives Nature Chose: sin, cos, eˣ, ln

Sine's derivative is cosine; eˣ is its own derivative. These are not coincidences — they are why these functions matter.

11–15 min · free · lesson 12 of 46

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By the end

  1. 01Justify the derivatives of sin x and cos x geometrically
  2. 02Explain e as the base whose exponential equals its own derivative
  3. 03Use d/dx ln x = 1/x

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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