A) \[\frac{-y}{x\,\left( y\,\cos y-1 \right)}\]
B) \[\frac{y}{v\,\cos \,y-1}\]
C) \[\frac{y}{y\,cos\,y+1}\]
D) \[\frac{y}{x\left( y\,\cos y-1 \right)}\]
Correct Answer: D
Solution :
\[{{e}^{\sin y}}=xy\Rightarrow \sin y=\operatorname{logx}+logy\] \[\Rightarrow \cos y\frac{dy}{dx}=\frac{1}{x}+\frac{1}{y}\frac{dy}{dx}\Rightarrow \frac{dy}{dx}\Rightarrow \left[ \cos y-\frac{1}{y} \right]=\frac{1}{x}\] \[\Rightarrow \frac{dy}{dx}=\frac{y}{x(ycosy-1)}\]
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