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

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 $\qquad$

Find the second order derivative of the function $\log (\log x)$.

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 $y = \sin(\sin x)$ and $y'' + f(x) \cdot y' + g(x) \cdot y = 0$,then $f(x) \cdot g(x) =$

If $y = \sin(m \sin^{-1} x)$, then $(1-x^2) y_2 - x y_1$ is equal to (Here, $y_n$ denotes $\frac{d^n y}{dx^n}$)