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📝 Definition of Derivative Function

📖 From Calculus • 3. The Derivation • 28 questions available

Practice MCQs for Definition of Derivative Function. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

8
Easy Questions
12
Medium Questions
8
Hard Questions

📝 Sample Questions

Q1. What is the definition of the derivative of \(f(x)\) with respect to \(x\)?

🔹 A. \(f'(x) = \lim_{h\to 0} \frac{f(x+h)-f(x)}{h}\)
🔹 B. \(f'(x) = \lim_{h\to 0} \frac{f(x)-f(x+h)}{h}\)
🔹 C. \(f'(x) = \lim_{h\to 0} \frac{f(x+h)+f(x)}{h}\)
🔹 D. \(f'(x) = \lim_{h\to 0} \frac{f(xh)-f(x)}{h}\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Find \(f'(x)\) for \(f(x) = x^3\) using the definition.

🔹 A. \(f'(x) = 3x^2\)
🔹 B. \(f'(x) = x^3\)
🔹 C. \(f'(x) = 3x\)
🔹 D. \(f'(x) = 3x^3\)

💡 Difficulty: medium | ✅ Correct: A

Q3. For \(f(x) = x^n\), where \(n\) is a positive integer, what is \(f'(x)\)?

🔹 A. \(f'(x) = nx^{n-1}\)
🔹 B. \(f'(x) = x^{n-1}\)
🔹 C. \(f'(x) = nx^n\)
🔹 D. \(f'(x) = (n-1)x^n\)

💡 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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