Questions in differentiation

Select	Question
	$\frac{d}{{dx}}\left\{ {\log \left( {\frac{{{e^x}}}{{1 + {e^x}}}} \right)} \right\} = $
	$\frac{d}{{dx}}\left[ {\frac{2}{\pi }\sin {x^0}} \right] = $
	$\frac{d}{{dx}}\left[ {\log \sqrt {\sin \sqrt {{e^x}} } } \right]$=
	If $f(x) = \,\|x\|,$then $f'(0) = $
	At $x = \sqrt {\frac{\pi }{2}} ,\frac{d}{{dx}}\cos (\sin {x^2})$=
	$\frac{d}{{dx}}[{\tan ^{ - 1}}(\cot x) + {\cot ^{ - 1}}(\tan x)] = $
	$\frac{d}{{dx}}[{e^{ax}}\cos (bx + c)]$=
	If $y = \log \log x$, then ${e^y}\frac{{dy}}{{dx}} = $
	If $y = {\sin ^{ - 1}}\left( {\frac{{19}}{{20}}x} \right) + {\cos ^{ - 1}}\left( {\frac{{19}}{{20}}x} \right)$, then $\frac{{dy}}{{dx}} = $
	If $y = (1 + {x^{1/4}})(1 + {x^{1/2}})(1 - {x^{1/4}})$, then $\frac{{dy}}{{dx}}$=