📝 MORE NOTATION; DIFFERENTIAL FORMULAS

📖 From Calculus • 4. Topics in Differentiation • 20 questions available

Practice MCQs for MORE NOTATION; DIFFERENTIAL FORMULAS. 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. In differential notation, the product rule is:

🔹 A. \(d(uv) = u\,dv + v\,du\)

🔹 B. \(d(uv) = du\,dv\)

🔹 C. \(d(uv) = u\,dv - v\,du\)

🔹 D. \(d(uv) = u\,du + v\,dv\)

💡 Difficulty: easy | ✅ Correct: A

Q2. The differential form of the quotient rule is:

🔹 A. \(d(u/v) = \frac{v\,du - u\,dv}{v^2}\)

🔹 B. \(d(u/v) = \frac{du}{v} - \frac{u}{v^2}dv\)

🔹 C. \(d(u/v) = \frac{v\,du + u\,dv}{v^2}\)

🔹 D. \(d(u/v) = \frac{u\,dv - v\,du}{v^2}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(d[f] = f'(x)dx\), then \(d[x^3\sin x]\) equals:

🔹 A. \((x^3\sin x + 3x^2\cos x)dx\)

🔹 B. \((x^3\cos x + 3x^2\sin x)dx\)

🔹 C. \((3x^2\sin x - x^3\cos x)dx\)

🔹 D. \((3x^2\sin x + x^3\cos x)dx\)

💡 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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