A) \[2\,\,\cos e{{c}^{3}}\,x\]
B) \[2\,{{\cot }^{2}}x-4{{x}^{2}}\,\cos e{{c}^{2}}\,{{x}^{2}}\]
C) \[2x\,\cot \,{{x}^{2}}\]
D) \[-2\,\cos e{{c}^{2}}\,x\]
Correct Answer: D
Solution :
We have, \[f\left( x \right)=2\,\log \,\sin \,x\] \[\Rightarrow \,f'\left( x \right)=2\,.\,\frac{1}{\sin \,x}.\,\cos x=2\,\cot \,x\] \[\Rightarrow \,f''\left( x \right)=-2\,\cos e{{c}^{2}}x\]
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