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

If $x=\sin \theta$ and $y=\sin^3 \theta$,then the value of $\frac{d^2 y}{dx^2}$ at $\theta=\frac{\pi}{2}$ is:

If $y = \tan^{-1} \sqrt{\frac{1 - \cos x}{1 + \cos x}}$,then the values of $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ respectively are

If $y = \tan(\log x)$,then $\frac{d^2 y}{d x^2} =$

If $y=A \cos n x+B \sin n x$,then $y_2+n^2 y$ is equal to

Suppose, $f(x)=e^{-\sqrt{x}}+e^{-\frac{1}{x^2}}$. If $f^{\prime \prime}(x)=\alpha \cdot \frac{e^{-\sqrt{x}}}{x}\left(1+\frac{1}{\sqrt{x}}\right)+\beta \cdot \frac{e^{-\frac{1}{x^2}}}{x^4}\left(3-\frac{2}{x^2}\right)$, then $(\alpha, \beta)=$