NCERT Class 12 · Ch 5 Exercise 5.3 · Q5
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 5
Find dy/dx for \(x^{2} + x y + y^{2} - 100 = 0\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(- \frac{2 x + y}{x + 2 y}\) where \(x + 2 y\)≠0.
- Differentiate the relation treating y as a function of x. The partial derivatives are Fₓ=\(2 x + y\) and Fᵧ=\(x + 2 y\).
- The chain rule gives Fₓ+Fᵧy′=0. Thus \(x + 2 y\)y′ = \(- 2 x - y\).
- At points where Fᵧ≠0, divide to obtain y′=\(- \frac{2 x + y}{x + 2 y}\). Points with Fᵧ=0 require a separate local-curve check.
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