If \[y={{(\sin x)}^{{{(\sin x)}^{(\sin x)......\infty }}}}\], then \[\frac{dy}{dx}=\]

\[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\]

\[\frac{{{y}^{2}}\cot x}{1-y\log \sin x}\]

\[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\]

\[\frac{y\cot x}{1-y\log \sin x}\]

\[\frac{y\cot x}{1+y\log \sin x}\]

If \[y={{(\sin x)}^{{{(\sin x)}^{(\sin x)......\infty }}}}\], then \[\

1.	If \[y={{(\sin x)}^{{{(\sin x)}^{(\sin x)......\infty }}}}\], then \[\frac{dy}{dx}=\]
A.	\[\frac{{{y}^{2}}\cot x}{1-y\log \sin x}\]
B.	\[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\]
C.	\[\frac{y\cot x}{1-y\log \sin x}\]
D.	\[\frac{y\cot x}{1+y\log \sin x}\]
Answer» B. \[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\]