Questions in differentiation

Select	Question
	If ${2^x} + {2^y} = {2^{x + y}},$then the value of $\frac{{dy}}{{dx}}$ at $x = y = 1$ is
	The derivative of $y = {x^{\ln x}}$ is
	If $y = \sqrt {x + \sqrt {x + \sqrt {x + ........{\rm{to}}} } } \infty \,,\,{\rm{then}}\frac{{dy}}{{dx}} = $
	If ${x^m}{y^n} = 2{(x + y)^{m + n}},$ the value of $\frac{{dy}}{{dx}}$ is
	If $x = {e^{y + {e^{y + ....t{\rm{o}}\,\,\infty }}}}$, $x > 0,$ then $\frac{{dy}}{{dx}}$ is
	If $y=\sin (2{{\sin }^{-1}}x),$then $\frac{dy}{dx}=$
	If $y={{\cos }^{-1}}\left( \frac{3\cos x+4\sin x}{5} \right)$, then $\frac{dy}{dx}=$
	$\frac{d}{dx}{{\cos }^{-1}}\frac{x-{{x}^{-1}}}{x+{{x}^{-1}}}$=
	If $y={{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}}+{{\sec }^{-1}}\frac{1+{{x}^{2}}}{1-{{x}^{2}}}$, then $\frac{dy}{dx}$=
	If $y={{\tan }^{-1}}\frac{x}{1+\sqrt{1-{{x}^{2}}}}+\sin \left\{ 2{{\tan }^{-1}}\sqrt{\left( \frac{1-x}{1+x} \right)} \right\}$,then $\frac{dy}{dx}$=