Unit 2
The derivative is defined as a limit and then made practical by rules. Building it from the difference quotient once is what makes the rules feel like shortcuts rather than magic.
12 problems · Questions and worked solutions.
Lesson 2.1 · AP 2.1–2.4
Build the derivative from average rates, connect its value to a tangent slope, and decide where differentiability fails.
Reading reference: Larson & Edwards §2.1
Read lesson →Lesson 2.2 · AP 2.5–2.8; 3.6
Differentiate standard function families and connect derivative values with rates and higher-order change.
Reading reference: Larson & Edwards §§2.2, 5.1, 5.4–5.5
Read lesson →Lesson 2.3 · AP 2.9–2.10; 3.1; 3.5
Recognize the structure of a function before choosing a rule, including products containing a composition.
Reading reference: Larson & Edwards §§2.3–2.4
Read lesson →Lesson 2.4 · AP 3.2–3.4; 3.6
Differentiate equations without solving for y, and use inverse relationships to find derivatives and tangent slopes.
Reading reference: Larson & Edwards §§2.5, 5.3, 5.6
Read lesson →Work through questions with a tutor and get help with the steps you find difficult.
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