A) \[1+\frac{\pi }{4}\]
B) \[\frac{1}{2}+\frac{\pi }{4}\]
C) \[\frac{1}{2}-\frac{\pi }{4}\]
D) 2
Correct Answer: B
Solution :
\[f(x)=x\,{{\tan }^{-1}}x\] On differentiating both sides w.r.t. \[x,\] we get \[f(x)=x\frac{1}{1+{{x}^{2}}}+{{\tan }^{-1}}x\] \[f{{(x)}_{x=1}}=\frac{1}{1+{{1}^{2}}}+{{\tan }^{-1}}1\] \[=\frac{1}{2}+\frac{\pi }{4}\]
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