Calculus I · Unit 2A · quiz

Special Functions Concept Quiz

Concept Quiz: Special Functions

• What limit is essential in proving $(\sin x)'=\cos x$ ? • Why is $(\cos x)'$ negative near $x=\pi/2$ ? • Why does $e^x$ differentiate to itself? • Distinguish the power rule for $x^n$ from the exponential rule for $a^x$ . • What is the domain of the derivative of $\ln|x|$ ? • Explain how the sign of $\ln a$ controls whether $a^x$ grows or decays.

After the explanation

Use the section idea

Reading lens

Connect each derivative formula to the function's characteristic growth, periodicity, or inverse relationship.

Mental model

Special-function rules preserve recognizable shapes while scaling them by a function-specific factor.

Decision

Identify the function family first, then check whether a composition requires the chain rule too.

Common trap

Using a power rule on an exponential or forgetting base and domain conditions for logarithms.

Check yourself

Can you distinguish a power, exponential, logarithmic, and trigonometric derivative at a glance?

Structured concept quiz

Special Functions 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 checkspecial-functions-concept-quiz-01

What limit is essential in proving $(\sin x)'=\cos x$ ?