Questions in differentiation

Select	Question
	If ${x^p}{y^q} = {(x + y)^{p + q}},$then $\frac{{dy}}{{dx}} = $
	If $y = {(\sin x)^{{{(\sin x)}^{(\sin x)......\infty }}}}$, then $\frac{{dy}}{{dx}} = $
	If $y = {({x^x})^x}$, then $\frac{{dy}}{{dx}}$=
	The differential equation satisfied by the function $y = \sqrt {\sin x + \sqrt {\sin x + \sqrt {\sin x + .....\infty } } } $, is
	If $y = {\left( {1 + \frac{1}{x}} \right)^x}$, then $\frac{{dy}}{{dx}} = $
	$\frac{d}{{dx}}({x^{{{\log }_e}x}}) = $
	If ${x^y} = {y^x},$then $\frac{{dy}}{{dx}} = $
	If $y = {x^{({x^x})}}$, then $\frac{{dy}}{{dx}} = $
	If $y = {x^{\sin x}},$then $\frac{{dy}}{{dx}} = $
	$\frac{d}{{dx}}\{ {(\sin x)^x}\} $=