Calc AB · U2
Differentiation: Definition and Properties
Define derivatives from limits, estimate slopes from data, and build the first major derivative-rule toolkit.
Test yourself
A focused, distraction-free run through 50 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 2.1
Defining Average and Instantaneous Rates of Change at a Point
Interpreting secant slopes and instantaneous rates through limiting average rates
Topic 2.2
Defining the Derivative of a Function and Using Derivative Notation
Connecting derivative notation with the limit definition of the derivative
Topic 2.3
Estimating Derivatives of a Function at a Point
Estimating tangent slopes from tables, graphs, and nearby average rates
Topic 2.4
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
Recognizing corners, jumps, cusps, vertical tangents, and slope mismatches
Topic 2.5
Applying the Power Rule
Differentiating powers, including negative and fractional exponents
Topic 2.6
Derivative Rules: Constant, Sum, Difference, and Constant Multiple
Combining basic derivative rules and interpreting derivatives of linear combinations
Topic 2.7
Derivatives of cos x, sin x, e^x, and ln x
Using core transcendental derivative rules without chain rule
Topic 2.8
The Product Rule
Differentiating products of functions and avoiding the common false rule $(fg)'=f'g'$
Topic 2.9
The Quotient Rule
Differentiating ratios of functions and reasoning about tangent slopes
Topic 2.10
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Using the remaining trigonometric derivative rules in direct and combined forms