📝 IMPLICIT DIFFERENTIATION

📖 From Calculus • 4. Topics in Differentiation • 34 questions available

Practice MCQs for IMPLICIT DIFFERENTIATION. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-14

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Q1. Using implicit differentiation, find \(\frac{dy}{dx}\) for \(x^2 + y^2 = 25\).

🔹 A. \(\frac{dy}{dx} = -\frac{y}{x}\)

🔹 B. \(\frac{dy}{dx} = \frac{x}{y}\)

🔹 C. \(\frac{dy}{dx} = \frac{y}{x}\)

🔹 D. \(\frac{dy}{dx} = -\frac{x}{y}\)

💡 Difficulty: easy | ✅ Correct: D

Q2. For \(x^3 + y^3 = 6xy\), \(\frac{dy}{dx} = \)

🔹 A. \(\frac{y - x^2}{y^2 - x}\)

🔹 B. \(\frac{x^2 - y}{y^2 - x}\)

🔹 C. \(\frac{y - x^2}{x^2 - y}\)

🔹 D. \(\frac{x^2 - y}{x - y^2}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. Find \(\frac{dy}{dx}\) for \(x^2 y + 3xy^3 - x = 3\).

🔹 A. \(\frac{1 - 2xy - 3y^3}{x^2 + 9xy}\)

🔹 B. \(\frac{2xy + 3y^3 - 1}{x^2 + 9xy^2}\)

🔹 C. \(\frac{1 - 2xy - 3y^3}{x^2 + 9xy^2}\)

🔹 D. \(\frac{2xy + 3y^3 - 1}{x^2 + 9xy}\)

💡 Difficulty: hard | ✅ Correct: C

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