📝 DERIVATIVES OF REAL POWERS OF x

📖 From Calculus • 4. Topics in Differentiation • 25 questions available

Practice MCQs for DERIVATIVES OF REAL POWERS OF x. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-14

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📝 Sample Questions

Q1. Find \(\frac{d}{dx}[x^{3.5}]\).

🔹 A. \(2.5x^{3.5}\)

🔹 B. \(3.5x^{3.5}\)

🔹 C. \(3.5x^{4.5}\)

🔹 D. \(3.5x^{2.5}\)

💡 Difficulty: easy | ✅ Correct: D

Q2. Find \(\frac{d}{dx}[\sqrt[3]{x^2}]\).

🔹 A. \(\frac{2}{3}x^{-2/3}\)

🔹 B. \(\frac{2}{3}x^{1/3}\)

🔹 C. \(\frac{1}{3}x^{-1/3}\)

🔹 D. \(\frac{2}{3}x^{-1/3}\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Find \(\frac{d}{dx}[x^{3/4}]\) at \(x = 16\).

🔹 A. \(\frac{1}{8}\)

🔹 B. \(\frac{3}{32}\)

🔹 C. \(\frac{3}{8}\)

🔹 D. \(\frac{3}{4}\)

💡 Difficulty: hard | ✅ Correct: B

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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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