MCQ
જો $f(x) = x\, {\tan ^{ - 1}}x$, તો $f'(1)=$
- A$1 + {\pi \over 4}$
- ✓${1 \over 2} + {\pi \over 4}$
- C${1 \over 2} - {\pi \over 4}$
- D$2$
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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