If f(x) = x , ^ - 1 x, then f'(1) = - Vidyadip

MCQ

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

A
$1 + {\pi \over 4}$
✓
${1 \over 2} + {\pi \over 4}$
C
${1 \over 2} - {\pi \over 4}$
D
$2$

✓

Answer

Correct option: B.

${1 \over 2} + {\pi \over 4}$

b
(b) $f(x) = x\,{\tan ^{ - 1}}x$

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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