📊 Chapter 2: Differentiation

AP Exam Weight: 25-35% | Multiple Choice: 10-14 questions | Free Response: Major focus in several questions

📚 Table of Contents

1. Definition
2. Basic Rules
3. Advanced Rules
4. Applications
5. Optimization

1. Definition of Derivative 📊

Understanding the Derivative

The derivative measures how quickly a function is changing at any point. Think of it as:

• The instantaneous speedometer in your car
• The slope of a mountain at a specific point
• The rate of population growth at a moment
• The sensitivity of temperature change

Limit Definition

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

Intuitive Understanding

• The derivative is a special limit
• We’re finding the slope of increasingly closer secant lines
• As h gets tiny (approaches 0), secant line becomes tangent line
• Think of zooming in until curve looks like a straight line

Process for Finding Limit Definition

1. Start with difference quotient