The number of solutions of $\tan ^{-1}\left(x+\frac{2}{x}\right)-\tan ^{-1}\left(\frac{4}{x}\right)-\tan ^{-1}\left(x-\frac{2}{x}\right)=0$ are

The derivative of $\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ w.r.t. $\tan ^{-1}\left(\frac{2 x \sqrt{1-x^2}}{1-2 x^2}\right)$ at $x=0$ is

If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\sec ^{-1}\left(\frac{1+x^2}{1-x^2}\right)$ then the value of $\frac{d y}{d x}$ at $x=\sqrt{3}$ is

$$ \cot ^{-1}\left(2 \cos \left(2 \operatorname{cosec}^{-1}(\sqrt{2})\right)\right)=\ldots $$