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📝 Derivatives And Inverse Hyperbolic Functions

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 2 questions available

Practice MCQs for Derivatives And 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. Solve for \(x\) in the equation \( \operatorname{asinh}(x)=1 \).

🔹 A. \( \frac{e- e^{-1}}{2} \)

🔹 B. \( \frac{e+ e^{-1}}{2} \)

🔹 C. \( \frac{e^{2}-1}{2e} \)

🔹 D. \( \frac{e^{2}+1}{2e} \)

💡 Difficulty: medium | ✅ Correct: C

Q2. Compute the second derivative of \( \operatorname{asinh}(x^{2}) \).

🔹 A. \( \frac{2}{\sqrt{x^{4}+1}}-\frac{4x^{4}}{(x^{4}+1)^{3/2}} \)

🔹 B. \( \frac{2}{\sqrt{x^{4}+1}}-\frac{4x^{2}}{(x^{4}+1)^{3/2}} \)

🔹 C. \( \frac{2}{\sqrt{x^{4}+1}}-\frac{8x^{2}}{(x^{4}+1)^{3/2}} \)

🔹 D. \( \frac{2}{\sqrt{x^{4}+1}}-\frac{8x^{4}}{(x^{4}+1)^{3/2}} \)

💡 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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