Rates of Change

Differentiation is the process of finding the derivative, which represents the rate of change of a function.

• The derivative of \( f(x) \), written \( f'(x) \), tells how \( f(x) \) changes as \( x \) changes.
• The power rule, product rule, quotient rule, and chain rule are essential techniques for finding derivatives.

Applications

• Finding the slope of a tangent line at a point
• Analyzing motion (velocity and acceleration)
• Solving optimization problems

Real-World Relevance

Derivatives are everywhere—speedometers, economics, biology, and more!