Calculus I · Unit 2A · quiz

Core Rules Concept Quiz

Concept Quiz: Core Rules

• Why is the derivative of a constant zero? • Explain the two contributions in the product rule. • Why is $(f/g)'$ not $f'/g'$ ? • When is expansion preferable to the product rule? • Rewrite $4/\sqrt[3]{x^2}$ in exponent form and differentiate. • Which rule is primary for $(x^2+1)^8$ , and why?

After the explanation

Use the section idea

Reading lens

Every rule is a compressed limit calculation; choose the structure before doing algebra.

Mental model

Sums contribute independently, products have two changing contributions, and quotients must account for a changing denominator.

Decision

Name the outermost algebraic structure, then apply the smallest rule set that preserves it.

Common trap

Applying a familiar rule to the wrong outer structure or simplifying after a differentiation error.

Check yourself

Can you justify the primary rule before writing the first derivative symbol?

Structured concept quiz

Core Rules Concept Quiz

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkcore-rules-concept-quiz-01

Why is the derivative of a constant zero?