📝 Derivatives of Compositions

📖 From Calculus • 3. The Derivation • 25 questions available

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

🔄 Last updated: 2026-07-13

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📝 Sample Questions

Q1. What is \(\frac{d}{dx}[\cos(x^3)]\)?

🔹 A. \(-3x^2\sin(x^3)\)

🔹 B. \(3x^2\sin(x^3)\)

🔹 C. \(-3x^2\cos(x^3)\)

🔹 D. \(-\sin(x^3)\)

💡 Difficulty: easy | ✅ Correct: A

Q2. If \(y = (x^2 + 3x)^5\), find \(\frac{dy}{dx}\).

🔹 A. \(5(x^2+3x)^4(2x+3)\)

🔹 B. \((x^2+3x)^4(2x+3)\)

🔹 C. \(5(x^2+3x)^4\)

🔹 D. \(5(x^2+3x)^5(2x+3)\)

💡 Difficulty: medium | ✅ Correct: A

Q3. What is \(\frac{d}{dx}[\tan(\sqrt{x})]\)?

🔹 A. \(\frac{\sec^2(\sqrt{x})}{2\sqrt{x}}\)

🔹 B. \(\frac{\sec^2(\sqrt{x})}{\sqrt{x}}\)

🔹 C. \(\frac{\sec(\sqrt{x})\tan(\sqrt{x})}{2\sqrt{x}}\)

🔹 D. \(\frac{-\sec^2(\sqrt{x})}{2\sqrt{x}}\)

💡 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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