AP Calculus 1 - Differentiation (Overview and Example Problems)
This video covers all AP Calculus AB standards related to derivatives and provides an overview of the idea of differentiation including the following:
Defining Derivatives and Differentiation
Relating Limits to Derivatives
Defining Differentiability
Estimating Derivatives at a Point
Derivative Rules (power rule, transcendental rules, product rule, quotient rule, chain rule)
Implicit Differentiation
Derivatives allow us to determine instantaneous rates of change. To develop understanding of how the definition of the derivative applies limits to average rates of change, the exploration of average rates of change over increasingly small intervals in needed. Limits are the foundation for differentiation (instantaneous rate of change). They are the basis for important definitions and for theorems that are used to solve realistic problems involving change and to justify conclusions.