If $y = \frac{\sqrt{x+1} + \sqrt{x-1}}{\sqrt{x+1} - \sqrt{x-1}}$, then $(x^2-1)^{3/2} \frac{d^2y}{dx^2} =$

If $y = \dfrac{\log_e x}{x}$, then $\dfrac{d^2y}{dx^2}$ is :

If $y = \log\left[\frac{x^2}{e^2}\right]$ then value of $\frac{d^2y}{dx^2}$ is :

If $y = \left(\log\left(x + \sqrt{x^2+a^2}\right)\right)^2$ and $x \neq \frac{1-a^2}{2}$, then $(x^2+a^2)\frac{d^2y}{dx^2} + x\frac{dy}{dx}$ is equal to:

If $x = at^2$ and $y = 2at$, then the value of $\frac{d^2y}{dx^2}$ is

( where t is a parameter )

Let $[x]$ denote the greatest integer function. Then match List-I with List-II:

$\frac{d}{dx}\left(e^{2\log_e x^3}\right)$ equals