If $y=\sin ^{-1}\left(\frac{\log x^2}{1+(\log x)^2}\right)$, then $\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\mathrm{at ~} x=1}=$

The value of $\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}+\frac{1}{2} \cos ^{-1} x$ is

$$\cos \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)\right]=$$

$\tan \left(\cos ^{-1} \frac{1}{\sqrt{2}}+\tan ^{-1} \frac{1}{2}\right)=$