Questions in differentiation

Select	Question
	The differential coefficient of the given function ${\log _e}\left( {\sqrt {\frac{{1 + \sin x}}{{1 - \sin x}}} } \right)$ with respect to x is
	$\frac{d}{{dx}}\left[ {\log \sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} } \right] = $
	$\frac{d}{{dx}}\left[ {{{\tan }^{ - 1}}\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} } \right] = $
	If $f(x) = {\tan ^{ - 1}}\left( {\frac{{\sin x}}{{1 + \cos x}}} \right)$,then $f'\left( {\frac{\pi }{3}} \right) = $
	$\frac{d}{{dx}}{e^{x\sin x}} = $
	$\frac{d}{{dx}}\{ \log (\sec x + \tan x)\} = $
	$\frac{d}{{dx}}(x{e^{{x^2}}}) = $
	$\frac{d}{{dx}}\left[ {\frac{{{e^{ax}}}}{{\sin (bx + c)}}} \right] = $
	If $y = \frac{{{e^x}\log x}}{{{x^2}}}$, then $\frac{{dy}}{{dx}} = $
	If $y = \frac{{{e^{2x}}\cos x}}{{x\sin x}},$then $\frac{{dy}}{{dx}} = $