If $e^{\left(\sinh ^{-1} 2+\cosh ^{-1} \sqrt{6}\right)}=(a+(b+\sqrt{c}) \sqrt{a}+b \sqrt{c})$, then $a+b+c=$

Consider the following statements

Assertion (A) For $x \in R-\{1\}$;

$$ \frac{d}{d x}\left(\tan ^{-1}\left(\frac{1+x}{1-x}\right)\right)=\frac{d}{d x}\left(\tan ^{-1} x\right) $$

Reason (R) For $x<1, \tan ^{-1}\left(\frac{1+x}{1-x}\right)=\frac{\pi}{4}+\tan ^{-1} x$, for

$$ x>1, \tan ^{-1}\left(\frac{1+x}{1-x}\right)=-\frac{3 \pi}{4}+\tan ^{-1} x $$

The correct answer is

If $y=\left(\sin ^{-1} x\right)^2$, then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

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