$\dfrac{d}{dx}\left[\sin^2\left\{\cot^{-1}\sqrt{\dfrac{1-x}{1+x}}\right\}\right] =$ ...

If $f(x) = \sqrt{x^2+1}, g(x) = \dfrac{x+1}{x^2+1}, h(x) = 2x - 3$, then $f'\left(h'(g'(x))\right) =$

If $\sqrt{y+x} + \sqrt{y-x} = c$ such that $\dfrac{dy}{dx} = f(x) - \sqrt{[f(x)]^2 - 1}$, then $f(x) =$ ____

If Rolle's theorem is applicable for the function $f(x) = \log\left(\dfrac{x^2+a}{x}\right)$ on $[3, 4]$ with $c \in (3, 4)$ such that $f'(c) = 0$, then the value of $f''(c)$ is