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 :
\[f(x)=x{{\tan }^{-1}}x\] Differentiating w.r.t x, we get \[f'(x)=x\frac{1}{1+{{x}^{2}}}+{{\tan }^{-1}}x\] Now put \[x=1\], then \[f'(1)=\frac{1}{2}+{{\tan }^{-1}}(1)=\frac{\pi }{4}+\frac{1}{2}\].
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