If $y=5 \cos x-3 \sin x$,then $\frac{d^2 y}{d x^2}=$ . . . . . . .

If $y = \sin x + e^x,$ then $\frac{d^2x}{dy^2} = $

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$, then $f^{\prime \prime}(-\pi)$ is equal to

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

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

If $y=\sin ^{-1} x,$ show that $\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=0$.