Continuity and Differentiability
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
If $y = \sqrt{\sin x + y}$, then $\dfrac{dy}{dx}$ is:
(a) $\dfrac{\cos x}{2y - 1}$
(b) $\dfrac{\cos x}{2y + 1}$
(c) $\dfrac{\sin x}{2y - 1}$
(d) $-\dfrac{\cos x}{2y - 1}$
Step-by-Step Solution
y^2 = sin x + y \implies 2y y' - y' = cos x \implies y' = cos x/(2y-1). [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\dfrac{\cos x}{2y - 1}$: 1.0 Mark
Correct Answer: $\dfrac{\cos x}{2y - 1}$
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