If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is

If $y=a x^{n+1}+b x^{-n}$, then $x^2 \frac{d^2 y}{d x^2}=$

If $y=\sin ^{-1}\left(\frac{3 x}{2}-\frac{x^3}{2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

If $\log (x+y)=\sin (x+y)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is