Calculus AB · Introduction to derivative definition, core differentiation rules, and the relationship between differentiability and continuity · 5 min read · Updated 2026-05-10
Differentiation: Definition and Fundamental Properties — AP Calculus AB
AP Calculus AB · Introduction to derivative definition, core differentiation rules, and the relationship between differentiability and continuity · 5 min read
1. Unit at a Glance
This unit builds on the limits you learned in Unit 1 to formalize the concept of instantaneous rate of change, which is the core of differentiation. We start with the formal definition of the derivative, then build up basic rules that let you skip tedious limit calculations for most common functions, turning derivative computation into a straightforward algebraic skill.
The unit progresses from conceptual understanding to rule application, so you will first master what a derivative is before learning the shortcuts you will use for the rest of the course. All subsequent units in AP Calculus AB depend on the skills you build in this unit.
Common Pitfalls
Why: Many students mix up the direction of the implication between differentiability and continuity.
Why: The specific order of terms in the quotient rule is easy to misremember, leading to sign errors.
Why: The derivative of cosine is the only core trig derivative with a negative sign, so it is often forgotten.