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📝 Derivative of a Product

📖 From Calculus • 3. The Derivation • 29 questions available

Practice MCQs for Derivative of a Product. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

11
Easy Questions
12
Medium Questions
6
Hard Questions

📝 Sample Questions

Q1. What is the derivative of \(f(x) = (3x^2 + 2)(x^3 - 1)\) using the product rule?

🔹 A. \(15x^4 + 6x^2 - 6x\)
🔹 B. \(15x^4 + 6x^2 + 6x\)
🔹 C. \(15x^4 - 6x^2 - 6x\)
🔹 D. \(9x^4 + 6x^2 - 6x\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Find \(\frac{d}{dx}[(x^2 + 1)\sqrt{x}]\).

🔹 A. \(\frac{5x^2 + 1}{2\sqrt{x}}\)
🔹 B. \(\frac{5x^2 - 1}{2\sqrt{x}}\)
🔹 C. \(\frac{3x^2 + 1}{2\sqrt{x}}\)
🔹 D. \(\frac{5x^2 + 1}{\sqrt{x}}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(y = (t^2 + 3)(t^3 - 2t)\), find \(\frac{d^2y}{dt^2}\).

🔹 A. \(20t^3 - 12t\)
🔹 B. \(20t^3 + 12t\)
🔹 C. \(20t^3 - 6t\)
🔹 D. \(15t^3 - 12t\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots📝 Areas and Limits📝 Continuity in Applications📝 Continuity of Compositions📝 Continuity of Inverse Functions
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