AP Calculus AB and BC - Differentiation: Definition and Basic Derivative Rules

Overview

Dive into a comprehensive 37-minute video review of Unit 2 in AP Calculus AB and BC, focusing on Differentiation: Definition and Basic Derivative Rules. Explore key concepts including average and instantaneous rates of change, defining derivatives, estimating derivatives at a point, and the connection between differentiability and continuity. Learn essential derivative rules such as the power rule, constant rule, sum and difference rules, and derivatives of common functions. Master the product and quotient rules, and understand how to find derivatives of trigonometric functions. Gain a solid foundation in calculus concepts with clear explanations and examples provided by math educator Krista King.

Syllabus

- Introduction.
- 2.1 Defining Average and Instantaneous Rates of Change at a Point.
- 2.2 Defining the Derivative of a Function and Using Derivative Notation.
- 2.3 Estimating Derivatives of a Function at a Point.
- 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist.
- 2.5 Applying the Power Rule.
- 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple.
- 2.7 Derivatives of cosx, sinx, ex, and lnx.
- 2.8 The Product Rule.
- 2.9 The Quotient Rule.
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions.
- Summary.