NCERT Class 12 · Ch 5 Exercise 5.3 · Q1
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 1
Find dy/dx for \(2 x + 3 y - \sin{\left(x \right)} = 0\).
💡 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: \(\frac{\cos{\left(x \right)} - 2}{3}\) where \(3\)≠0.
- Differentiate the relation treating y as a function of x. The partial derivatives are Fₓ=\(2 - \cos{\left(x \right)}\) and Fᵧ=\(3\).
- The chain rule gives Fₓ+Fᵧy′=0. Thus \(3\)y′ = \(\cos{\left(x \right)} - 2\).
- At points where Fᵧ≠0, divide to obtain y′=\(\frac{\cos{\left(x \right)} - 2}{3}\). Points with Fᵧ=0 require a separate local-curve check.
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