question_answer

If \[f\,\,(x)={{\tan }^{-1}}\,\,\left( \frac{\sin \,\,x}{1+\cos \,\,x} \right),\]  then \[f'\,\,\left( \frac{\pi }{3} \right)=\]

A)  \[\frac{1}{2\,\,(1+\cos x)}\]                   

B)  \[\frac{1}{2}\]

C)  \[\frac{1}{4}\]                         

D)  \[\frac{1}{2\,\,{{(1+\sin x)}^{2}}}\]

E)  None of these