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📝 Derivatives And Integrals Involving Inverse Hyperbolic Functions

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 21 questions available

Practice MCQs for Derivatives And Integrals Involving Inverse Hyperbolic Functions. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What is the derivative of \( \operatorname{asinh}(x) \)?

🔹 A. \( \frac{1}{\sqrt{x^{2}+1}} \)

🔹 B. \( \frac{x}{\sqrt{x^{2}+1}} \)

🔹 C. \( \sqrt{x^{2}+1} \)

🔹 D. \( \ln\!\left(x+\sqrt{x^{2}+1}\right) \)

💡 Difficulty: easy | ✅ Correct: A

Q2. Find the derivative of \( \operatorname{acosh}(x) \).

🔹 A. \( \frac{1}{\sqrt{x-1}\sqrt{x+1}} \)

🔹 B. \( \frac{x}{\sqrt{x^{2}-1}} \)

🔹 C. \( \frac{1}{\sqrt{x^{2}-1}} \)

🔹 D. \( \frac{1}{x\sqrt{x^{2}-1}} \)

💡 Difficulty: medium | ✅ Correct: C

Q3. A particle is acted on by a variable force \(F(x)=\operatorname{asinh}(x)\) (in newtons) while moving from \(x=0\) to \(x=1\) meters. What is the work done?

🔹 A. \( \operatorname{asinh}(1)-\sqrt{2}+C \)

🔹 B. \( \frac{1}{2}\bigl[\operatorname{asinh}(1)\bigr]^{2} \)

🔹 C. \( \operatorname{asinh}(1)+\sqrt{2} \)

🔹 D. \( \frac{1}{2}\bigl[\operatorname{asinh}(1)\bigr]^{2}+C \)

💡 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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