📝 Generalized Derivative Formulas

📖 From Calculus • 3. The Derivation • 27 questions available

Practice MCQs for Generalized Derivative Formulas. 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. The generalized derivative formula for \(\sin u\) is:

🔹 A. \(\cos u \frac{du}{dx}\)

🔹 B. \(-\sin u \frac{du}{dx}\)

🔹 C. \(\sin u \frac{du}{dx}\)

🔹 D. \(\cos u\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Find \(\frac{d}{dx}[\tan(x^2+1)]\) using the generalized formula.

🔹 A. \(2x\sec^2(x^2+1)\)

🔹 B. \(2x\sec(x^2+1)\tan(x^2+1)\)

🔹 C. \(2x\csc^2(x^2+1)\)

🔹 D. \(\sec^2(x^2+1)\)

💡 Difficulty: medium | ✅ Correct: A

Q3. What is \(\frac{d}{dx}[\sqrt{x^3+\csc x}]\) using the generalized formula?

🔹 A. \(\frac{3x^2-\csc x\cot x}{2\sqrt{x^3+\csc x}}\)

🔹 B. \(\frac{3x^2+\csc x\cot x}{2\sqrt{x^3+\csc x}}\)

🔹 C. \(\frac{3x^2-\csc^2 x}{2\sqrt{x^3+\csc x}}\)

🔹 D. \(\frac{3x^2-\csc x\cot x}{\sqrt{x^3+\csc x}}\)

💡 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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