Questions in differentiation

Select	Question
	If $y = x{\rm{ }}\left[ {\left( {\cos \frac{x}{2} + \sin \frac{x}{2}} \right){\rm{ }}\left( {\cos \frac{x}{2} - \sin \frac{x}{2}} \right) + \sin x} \right] + \frac{1}{{2\sqrt x }}$, then $\frac{{dy}}{{dx}} = $
	The differential coefficient of ${a^x} + \log x.\sin x$is
	$\frac{d}{{dx}}{\tan ^{ - 1}}\left( {\frac{{ax - b}}{{bx + a}}} \right) = $
	$\frac{d}{{dx}}\left( {{{\tan }^{ - 1}}\sqrt {\frac{{1 + \cos \frac{x}{2}}}{{1 - \cos \frac{x}{2}}}} } \right)$is equal to
	$\frac{d}{{dx}}\sqrt {\frac{{1 - \sin 2x}}{{1 + \sin 2x}}} = $
	If $y = \sqrt {(1 - x)(1 + x)} $, then
	$\frac{d}{{dx}}\left( {\frac{{{{\cot }^2}x - 1}}{{{{\cot }^2}x + 1}}} \right) = $
	If $f(x) = x{\tan ^{ - 1}}x$, then $f'(1)$=
	If $y = {\log _{10}}x + {\log _x}10 + {\log _x}x + {\log _{10}}10,$then $\frac{{dy}}{{dx}} = $
	If $y = b\cos \log {\left( {\frac{x}{n}} \right)^n}$, then $\frac{{dy}}{{dx}} = $