Module 2: The Derivative
Discover the central concept of differential calculus: the derivative as an instantaneous rate of change, its formal definition, and basic rules for computing derivatives.
Learning Objectives
By the end of this module, you will be able to:
- Compute average and instantaneous rates of change
- Apply the limit definition of the derivative
- Interpret the derivative as the slope of the tangent line
- Determine where a function is differentiable
- Use the power, constant, sum, and difference rules
Module Lessons
1
Average and Instantaneous Rates of Change
Understand secant lines, difference quotients, and the transition to instantaneous rate of change.
30-40 minutes
2
The Derivative: Definition and Notation
Learn the formal limit definition of the derivative and the various notations used in calculus.
35-45 minutes
3
Differentiability and Local Linearity
Explore when derivatives exist, where they fail, and how differentiable functions look locally linear.
25-35 minutes
4
Basic Differentiation Rules
Master the power rule, constant rule, sum and difference rules, and derivatives of e^x and ln x.
30-40 minutes
After the Lessons
Practice Problems
10 problems covering rates of change, limit definition, and basic rules.
Practice Problems