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📝 Alternative Chain Rule

📖 From Calculus • 3. The Derivation • 24 questions available

Practice MCQs for Alternative Chain Rule. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

8
Easy Questions
10
Medium Questions
6
Hard Questions

📝 Sample Questions

Q1. In the alternative chain rule \(\frac{d}{dx}[f(g(x))] = f'(g(x))g'(x)\), \(f\) is called the:

🔹 A. Outside function
🔹 B. Inside function
🔹 C. Composite function
🔹 D. Derivative function

💡 Difficulty: easy | ✅ Correct: A

Q2. If \(h(x) = \sqrt{\tan x}\), what is \(h'(x)\) using the alternative chain rule?

🔹 A. \(\frac{\sec^2 x}{2\sqrt{\tan x}}\)
🔹 B. \(\frac{\tan^2 x}{2\sqrt{\tan x}}\)
🔹 C. \(\frac{1}{2\sqrt{\tan x}}\)
🔹 D. \(\frac{\sec^2 x}{\sqrt{\tan x}}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(f(2)=3\), \(f'(2)=4\), \(g(3)=5\), and \(g'(3)=6\), find \((f\circ g)'(3)\).

🔹 A. \(24\)
🔹 B. \(20\)
🔹 C. \(18\)
🔹 D. \(12\)

💡 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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