A) \[\frac{1}{2}\frac{\cos \sqrt{\sin x+\cos x}}{\sqrt{\sin x+\cos x}}\]
B) \[\frac{\cos \sqrt{\sin x+\cos x}}{\sqrt{\sin x+\cos x}}\]
C) \[\frac{1}{2}\frac{\cos \sqrt{\sin x+\cos x}}{\sqrt{\sin x+\cos x}}.(\cos x-\sin x)\]
D) None of these
Correct Answer: C
Solution :
\[y=\sin (\sqrt{\sin x+\cos x})\] \[\frac{dy}{dx}=\frac{1}{2}\frac{\cos (\sqrt{\sin x+\cos x})}{\sqrt{\sin x+\cos x}}(\cos x-\sin x)\].
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