Let $f(x)=e^x$, $g(x)=\sin^{-1} x$ and $h(x)=f(g(x))$, then $\frac{h'(x)}{h(x)}$ is equal to

$\frac{d}{dx}(e^{x \log x} + e^3) = $ . . . . . .

For $x^2-4 \neq 0$,the value of $\frac{d}{d x}\left[\log \left\{e^x\left(\frac{x-2}{x+2}\right)^{\frac{3}{4}}\right\}\right]$ at $x=3$ is

If $y = \log \left[a^{3x} \left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]$,then $\frac{dy}{dx} = $

$\frac{d}{dx} \left[ \log \left\{ e^x \left( \frac{x - 2}{x + 2} \right)^{3/4} \right\} \right]$ is equal to

Consider the following statements:
Statement $1$: If $y = \log_{10} x + \log_{e} x$,then $\frac{dy}{dx} = \frac{\log_{10} e}{x} + \frac{1}{x}$.
Statement $2$: $\frac{d}{dx}(\log_{10} x) = \frac{\log x}{\log 10}$ and $\frac{d}{dx}(\log_{e} x) = \frac{\log x}{\log e}$.