If $y = \frac{1}{x} + \cos 2x$, then $\frac{d^2y}{dx^2}$ is equal to

Let $f(x)$ and $g(x)$ be two functions having finite non-zero $3^{rd}$ order derivatives $f'''(x)$ and $g'''(x)$ for all $x \in R$. If $f(x)g(x) = 1$ for all $x \in R$,then $\frac{f'''}{f'} - \frac{g'''}{g'}$ is equal to

If $y = \sqrt{x^2 + 8x + 3}$, then the value of $\frac{d^2y}{dx^2}$ at $x = 3$ is

If $y=\frac{\log _e x}{x}$ and $z=\log _e x$, then $\frac{d^2 y}{d z^2}+\frac{d y}{d z}$ is equal to

$\frac{d^2 x}{d y^2}$ equals

If $y=2 x^{n+1}+\frac{3}{x^{n}}$,then $x^{2} \frac{d^{2} y}{d x^{2}}$ is