If $f(x)=\log _e\left(e^{2 x}\left(\frac{3 x+5}{5-3 x}\right)^{\frac{2}{3}}\right)$, $x \neq \frac{-5}{3}, \frac{5}{3}$, then the value of $\frac{d f}{d x}$ at $x=1$ is

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

$\frac{d}{dx} [\log(\cos x)]$

$\frac{d}{dx} \left( \log \left( \sqrt{x + \sqrt{x^2 + a^2}} \right) \right) = $

If $y=e^{\log _{e}\left[1+x+x^{2}+\ldots\right]}$,then $\frac{d y}{d x}$ is equal to

If $y = f \left( \frac{3 + 2x}{3 - 2x} \right)$, where $f(x) = \tan(\log x)$ and $\frac{dy}{dx} = \left( \frac{A}{B + Cx^2} \right) \cdot \sec^2 \left( \log \left( \frac{3 + 2x}{3 - 2x} \right) \right)$, then the respective values of $A, B$ and $C$ are ......