The range of the real value function $f(x)=\sin ^{-1}\left(\sqrt{x^2+x+1}\right)$ is

$$ \tan ^{-1} \frac{3}{5}+\tan ^{-1} \frac{6}{41}+\tan ^{-1} \frac{9}{191}= $$

If $2 \tanh ^{-1} x=\sinh ^{-1}\left(\frac{4}{3}\right)$, then $\cosh ^{-1}\left(\frac{1}{x}\right)=$

If $f(x)=\sqrt{\cos ^{-1} \sqrt{1-x^2}}$, then $f^{\prime}\left(\frac{1}{2}\right)=$