Question

If $f(x)=x{\tan }^{-1}x,$ then $f^{\prime }(1)$ equals

• A. $\frac{1}{2}+\frac{\pi }{4}$
• B. $-\frac{1}{2}+\frac{\pi }{4}$
• C. $-\frac{1}{2}-\frac{\pi }{4}$
• D. $\frac{1}{2}-\frac{\pi }{4}$

Answer 1

Answer: (A)

$f^{\prime }\left(x\right)=\frac{x}{1+x^2}+{\tan }^{-1}x$
$\Rightarrow f^{\prime }\left(1\right)=\frac{1}{2}+{\tan }^{-1}1=\frac{1}{2}+\frac{\pi }{4}.$