A) \[\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{1-\sin x}-\frac{1}{2x} \right]\]
B) \[\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\]
C) \[\frac{2{{(x-\sin x)}^{1/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\]
D) None of these
Correct Answer: B
Solution :
\[\log y=\log 2+\frac{3}{2}\log (x-\sin x)-\frac{1}{2}\log x\] \[\Rightarrow \frac{dy}{dx}=y\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\].
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