If f(x)=2x+cot-1x+log1+x2-x, then f(x)

f'(x)=2-11+x2+x1+x2-11+x2-x =2-11+x2-11+x2>0 In [0,π]

f'(x)=2-11+x2+x1+x2-11+x2-x =2-11+x2-11+x2>0 In [0,π]

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$If f (x) = 2 x + \cot^{- 1} x + \log (\sqrt{1 + x^{2}} - x), then f (x)$

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$increases in [0, π)$

$neither increases nor decreases in (0, π)$

4) None of these

$decreases in [0, π)$

answer is A.

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$f^{'} (x) = 2 - \frac{1}{1 + x^{2}} + \frac{\frac{x}{\sqrt{1 + x^{2}}} - 1}{\sqrt{1 + x^{2}} - x}$

$= 2 - \frac{1}{1 + x^{2}} - \frac{1}{\sqrt{1 + x^{2}}} > 0$

$In [0, π]$

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