Let $f$ be a twice differentiable function such that $f^{\prime \prime}(x) = -f(x)$,$f^{\prime}(x) = g(x)$ and $h(x) = [f(x)]^2 + [g(x)]^2$. If $h(5) = 1$,then $h(10)$ is $\qquad$

Let $f : S \rightarrow S$ where $S =(0, \infty)$ be a twice differentiable function such that $f(x+1) = xf(x)$. If $g : S \rightarrow R$ is defined as $g(x) = \log_{e} f(x)$,then the value of $|g''(5) - g''(1)|$ is equal to:

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

If $y = \frac{(\sin^{-1} x)^2}{2}$,then $(1-x^2) y_2 - x y_1 = $

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

$\frac{d^n}{dx^n}(\log x) =$