📝 LOGARITHMIC DIFFERENTIATION

📖 From Calculus • 4. Topics in Differentiation • 28 questions available

Practice MCQs for LOGARITHMIC DIFFERENTIATION. 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. What is the first step in logarithmic differentiation?

🔹 A. Solve for \(y\) explicitly

🔹 B. Differentiate both sides directly

🔹 C. Apply the product rule

🔹 D. Take the natural logarithm of both sides

💡 Difficulty: easy | ✅ Correct: D

Q2. Use logarithmic differentiation to find \(y'\) for \(y = x\sqrt[3]{1+x^2}\).

🔹 A. \(x\sqrt[3]{1+x^2}\left[\frac{1}{x} + \frac{x}{1+x^2}\right]\)

🔹 B. \(x\sqrt[3]{1+x^2}\left[\frac{1}{x} + \frac{2x}{3(1+x^2)}\right]\)

🔹 C. \(x\sqrt[3]{1+x^2}\left[\frac{1}{x} + \frac{2x}{1+x^2}\right]\)

🔹 D. \(x\sqrt[3]{1+x^2}\left[\frac{1}{x} + \frac{2x}{3(1+x^2)}\right]\)

💡 Difficulty: medium | ✅ Correct: B

Q3. Use logarithmic differentiation to find \(y'\) for \(y = \frac{x^2\sqrt[3]{7x-14}}{(1+x^2)^4}\).

🔹 A. \(y\left[\frac{2}{x} + \frac{1}{3x-6} - \frac{8x}{1+x^2}\right]\)

🔹 B. \(y\left[\frac{2}{x} - \frac{7}{3(7x-14)} + \frac{8x}{1+x^2}\right]\)

🔹 C. \(y\left[\frac{2}{x} + \frac{7}{3(7x-14)} + \frac{8x}{1+x^2}\right]\)

🔹 D. \(y\left[\frac{2}{x} + \frac{7}{3(7x-14)} - \frac{8x}{1+x^2}\right]\)

💡 Difficulty: hard | ✅ Correct: D

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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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