Introduction to Derivatives

A derivative measures the rate of change of a function with respect to its variable. It is one of the most important concepts in calculus.

Definition

Geometric Interpretation

Finding Derivatives from First Principles

Example: Derivative of

Example: Derivative of

Notation

Practice Problems

1. Find the derivative of from first principles.
2. Find the derivative of from first principles.
3. Find the slope of the tangent to at .
4. If , find .