If the function $y = \sin^{-1} x$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}$ is equal to

If $y = (x^2 - 1)^m$,then the $(2m)^{th}$ differential coefficient of $y$ is

If $x^x y^y=e^e$,then $\left(\frac{d^2 y}{d x^2}\right)_{(e, e)}=$

If $y = \sin^2 \alpha + \cos^2(\alpha + \beta) + 2 \sin \alpha \sin \beta \cos(\alpha + \beta)$,then find $\frac{d^3y}{d\alpha^3}$ (keeping $\beta$ as a constant).

If $y = \frac{\log x}{x}$,then the value of $x^2 \frac{d^2 y}{d x^2} + 3x \frac{d y}{d x} + y$ at the point $(\sqrt[3]{e}, \frac{\log(\sqrt[3]{e})}{\sqrt[3]{e}})$ is

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 the value of $h(10)$ is