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