A) \[{{\tan }^{-1}}\{{{(\log x)}^{n}}\}\]
B) 0
C) \[\frac{1}{2}\]
D) None of these
Correct Answer: B
Solution :
We have \[y={{\tan }^{-1}}\left( \frac{\log e-\log {{x}^{2}}}{\log e+\log {{x}^{2}}} \right)+{{\tan }^{-1}}\left( \frac{3+2\log x}{1-6\log x} \right)\] \[={{\tan }^{-1}}\left( \frac{1-2\log x}{1+2\log x} \right)+{{\tan }^{-1}}\left( \frac{3+2\log x}{1-6\log x} \right)\] \[={{\tan }^{-1}}1-{{\tan }^{-1}}(2\log x)+{{\tan }^{-1}}3+{{\tan }^{-1}}(2\log x)\] \[\Rightarrow y={{\tan }^{-1}}1+{{\tan }^{-1}}3\Rightarrow \frac{dy}{dx}=0\Rightarrow \frac{{{d}^{n}}y}{d{{x}^{n}}}=0.\]You need to login to perform this action.
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