Class 12 Continuity And Differentiability · Long Answer3 Marksimplicit_differentiation
Class 12 Maths · Continuity And Differentiability · Long Answer #151
If e^y(x+1)=1, show y″=(y′)².
✅ Step-by-Step Solution
Final Answer: y″=(y′)²
- The real equation requires x+1>0 and gives y=−ln(x+1).
- Differentiate: y′=−1/(x+1).
- Differentiate again: y″=1/(x+1)², while (y′)²=1/(x+1)².
- Therefore y″=(y′)² on x>−1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The real equation requires x+1>0 and gives y=−ln(x+1).
- [1 mark] Differentiate: y′=−1/(x+1).
- [1 mark] Differentiate again: y″=1/(x+1)², while (y′)²=1/(x+1)².
- [0.5 marks] Therefore y″=(y′)² on x>−1.
Master Chapter 5: Continuity And Differentiability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
← Previous Question
If (ax+b)e^(y/x)=x on a differentiable real branch with x≠0 and…
Next Question →For x=\(a \left(t - \sin{\left(t \right)}\right)\), y=\(a…
More Practice Questions in Continuity And Differentiability
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?