A) \[2\]
B) \[1\]
C) \[0\]
D) \[-1\]
Correct Answer: C
Solution :
| \[y={{\tan }^{-1}}\left( \frac{{{\log }_{e}}(e/{{x}^{2}})}{{{\log }_{e}}(e{{x}^{2}})} \right)+{{\tan }^{-1}}\left( \frac{3+2{{\log }_{e}}x}{1-6{{\log }_{e}}x} \right)\] |
| \[={{\tan }^{-1}}\left( \frac{1-2{{\log }_{e}}x}{1+2{{\log }_{e}}x} \right)+{{\tan }^{-1}}\left( \frac{3+2{{\log }_{e}}x}{1-3.2\,lo{{g}_{e}}x} \right)\] |
| \[={{\tan }^{-1}}(a)-{{\tan }^{-1}}(2{{\log }_{e}}x)\]\[+{{\tan }^{-1}}(c)+ta{{n}^{-1}}(2{{\log }_{e}}x)\] |
| \[={{\tan }^{-1}}(a)+{{\tan }^{-1}}(c)\] |
| \[\therefore \,\,\frac{dy}{dx}=0\] |
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