Differentiate $\log _a x$ with respect to $a^x$

If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, then $f^{\prime}(0)=$

If $y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}, \quad$ then $2 x y \frac{d y}{d x}$ is equal to

If $y=\sin ^{-1}\left(\frac{1}{\sqrt{x+1}}\right)$ then $\frac{d y}{d x}=$