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

If $y=2 \sin x+3 \cos x$ and $y+A \frac{d^2 y}{d x^2}=B$,then the values of $A$ and $B$ are respectively:

If $y = e^{nx}$,then $\left( \frac{d^2y}{dx^2} \right) \left( \frac{d^2x}{dy^2} \right)$ is equal to

If $f(x)=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^{2}}\right)}{\log \left(e x^{2}\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$ then the value of $f^{\prime \prime}(x)$ is equal to

If $\cos ^{-1}\left(\frac{y}{2}\right)=\log _{e}\left(\frac{x}{5}\right)^{5}$ and $|y| < 2$,then which of the following is true?

If $y=f(\cosh x)$ and $f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)$,then $\frac{d^2 y}{d x^2}=$