AP Unit 2: Differentiation: Definition and Fundamental Properties
Find these readings by topic
This earlier reading list remains available with its complete tasks. The current book places these resources in the following topic chapters:
- Derivatives as rates of change →
Explain and estimate an instantaneous rate, decide when it exists, and interpret its signed units.
- Differentiation tools →
Choose derivative rules for explicit, composite, inverse, and implicit functions while respecting domains.
Build derivatives from limiting rates, connect them to tangent lines, then use justified derivative rules with domains intact.
Follow the topics below, then try the 30 unit problems before opening the separate step-by-step solutions.
Course outline · Teacher guidance
This unit includes the shared AB core explicitly inside the BC book, with BC extensions where required. Each shared topic links to its AB source.
- 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 cos x, sin x, e^x, and ln x ↗
- 2.8 The Product Rule ↗
- 2.9 The Quotient Rule ↗
- 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions ↗