If \[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}} \right)}{\log (e{{x}^{2}})} \right\}+{{\tan }^{-1}}\left( \frac{3+2\log x}{1-6\log x} \right)\], then \[\frac{{{d}^{n}}y}{d{{x}^{n}}}\] is \[(n\ge 1)\]

\[{{\tan }^{-1}}\{{{(\log x)}^{n}}\}\]

If \[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}}

1.	If \[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}} \right)}{\log (e{{x}^{2}})} \right\}+{{\tan }^{-1}}\left( \frac{3+2\log x}{1-6\log x} \right)\], then \[\frac{{{d}^{n}}y}{d{{x}^{n}}}\] is \[(n\ge 1)\]
A.	\[{{\tan }^{-1}}\{{{(\log x)}^{n}}\}\]
B.	0
C.	\[\frac{1}{2}\]
D.	None of these
Answer» C. \[\frac{1}{2}\]

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If \[f(x)={{\tan }^{-1}}\left\{ \frac{\log \left( \frac{e}{{{x}^{2}}} \right)}{\log (e{{x}^{2}})} \right\}+{{\tan }^{-1}}\left( \frac{3+2\log x}{1-6\log x} \right)\], then \[\frac{{{d}^{n}}y}{d{{x}^{n}}}\] is \[(n\ge 1)\]

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