If $y = 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!} - \dots$,then $\frac{d^2y}{dx^2} = $

If $f(x)$ and $g(x)$ are twice differentiable functions satisfying $f''(x) = g''(x)$, $f'(1) = 2g'(1) = 4$ and $f(2) = 3g(2) = 9$, then the value of $f(x) - g(x)$ at $x = 4$ is:

If $y = \log_e(\log_e x)$ for $x > 1$,then $\frac{d^2 y}{dx^2} = $ . . . . . . .

If $y=\log \left(x-\sqrt{x^2-1}\right)$, then $\left(x^2-1\right) y^{\prime \prime}+x y^{\prime}$ is equal to:

If $y = \sin(\log_e x)$, then $x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx}$ is equal to

If $y = \operatorname{Sec}^{-1} x$, then $\frac{d^2 y}{d x^2} = $