What is the derivative of x · sin(x) using the product rule?

A sin(x) + x·cos(x)

B x·cos(x)

C sin(x)·cos(x)

D cos(x) − x·sin(x)

✓ Correct Answer: Option A

Product rule: d/dx[x·sin(x)] = 1·sin(x) + x·cos(x) = sin(x) + x·cos(x).

💡 Why is A) the correct answer?

The correct answer to the question "What is the derivative of x · sin(x) using the product rule?" is Option A: sin(x) + x·cos(x).

The other options — B) x·cos(x), C) sin(x)·cos(x), D) cos(x) − x·sin(x) — are incorrect for this AP Exam Prep question. As explained above: Product rule: d/dx[x·sin(x)] = 1·sin(x) + x·cos(x) = sin(x) + x·cos(x).

📚 About This AP Exam Prep Practice Question

This 2-level AP Exam Prep question from the AP Calculus topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free AP Exam Prep practice test or use flashcards for spaced repetition review.

Practice AP Exam Prep Quizzes → Browse All Questions Study Flashcards

What is the derivative of x · sin(x) using the product rule?

✓ Correct Answer: Option A

📚 About This AP Exam Prep Practice Question

Related AP Exam Prep Questions