Question

If $f(x)=x{\tan }^{-1}x$, then $f^{\prime }(1)$ is equal to :

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

Answer 1

Answer: (B)

$f(x)=x{\tan }^{-1}x$
On differentiating both sides w.r.t. $x$, we get
$f^{\prime }(x)=x\frac{1}{1+x^2}+{\tan }^{-1}x$
$f^{\prime }(x{)}_{x=1}=\frac{1}{1+1^2}+{\tan }^{-1}1$
$=\frac{1}{2}+\frac{\pi }{4}$