NCERT Class 12 · Ch 5 Exercise 5.3 · Q3
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.3 Question 3
Find dy/dx for \(a x + b y^{2} - \cos{\left(y \right)} = 0\).
💡 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: \(- \frac{a}{2 b y + \sin{\left(y \right)}}\) where \(2 b y + \sin{\left(y \right)}\)≠0.
- Differentiate the relation treating y as a function of x. The partial derivatives are Fₓ=\(a\) and Fᵧ=\(2 b y + \sin{\left(y \right)}\).
- The chain rule gives Fₓ+Fᵧy′=0. Thus \(2 b y + \sin{\left(y \right)}\)y′ = \(- a\).
- At points where Fᵧ≠0, divide to obtain y′=\(- \frac{a}{2 b y + \sin{\left(y \right)}}\). Points with Fᵧ=0 require a separate local-curve check.
Master Chapter 5: Continuity And Differentiability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
← Previous Question
Find dy/dx for \(2 x + 3 y - \sin{\left(y \right)} = 0\).
Next Question →Find dy/dx for \(x y + y^{2} - y - \tan{\left(x \right)} = 0\).
All Questions in Continuity And Differentiability — Exercise 5.3
Related Questions in Continuity And Differentiability
Class 12 Continuity And Differentiability · Mcq Single Correct
For k<0, define f(x)=(1−cos(kx))/(x sin x) for nonzero x near 0, and f(0)=1/2. Find k for…
Class 12 Continuity And Differentiability · Mcq Single Correct
Near π/2, f(x)=k cos x/(π−2x) for x≠π/2 and f(π/2)=3. Find k for continuity.
Class 12 Continuity And Differentiability · Mcq Single Correct
Find the full set of real inputs excluded from the natural domain of cot x (its poles).
Class 12 Continuity And Differentiability · Mcq Single Correct
How many real inputs are excluded from the original formula f(x)=(x−1)/[x(x²−1)]?
Class 12 Continuity And Differentiability · Mcq Single Correct
For x≠0, f(x)=(e^(3x)−e^(−5x))/x, and f(0)=k. Find k for continuity at 0.
Class 12 Continuity And Differentiability · Mcq Single Correct
Let f(x)=x/|x| for x<0 and f(x)=−1 for x≥0. What is its complete continuity set?