Continuity and Differentiability
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
If $y = \tan^{-1}\left(\dfrac{\sin x}{1 + \cos x}\right)$, find $\dfrac{dy}{dx}$.
Step-by-Step Solution
Given: Problem statement: If $y = \tan^{-1}\left(\dfrac{\sin x}{1 + \cos x}\right)$, find $\dfrac{dy}{dx}$.
Step 1: Apply limit / differentiation rule:
Evaluate LHL/RHL or apply chain rule. [1.0 Mark]
Step 2: Simplify and evaluate final answer:
Obtain final derivative / continuity constant. [1.0 Mark]
Conclusion: Result verified.
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🎯 Official CBSE Marking Scheme:
Applying differentiation rule / limit condition: 1.0 Mark
Evaluating correct final derivative / constant: 1.0 Mark
Correct Answer:
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