Questions in differentiation

Select	Question
	If ${{x}^{x}}{{y}^{y}}{{z}^{z}}=c$, then $\frac{\partial z}{\partial x}=$
	If $u=x{{y}^{2}}{{\tan }^{-1}}\left( \frac{y}{x} \right)$, then $x{{u}_{x}}+y{{u}_{y}}=$
	If ${{z}^{2}}=\frac{{{x}^{1/2}}+{{y}^{1/2}}}{{{x}^{1/3}}+{{y}^{1/3}}}$ then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=$
	If $u={{\tan }^{-1}}(x+y),$ then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=$
	If $u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}$, then ${{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}=$
	If $u={{x}^{2}}{{\tan }^{-1}}\frac{y}{x}-{{y}^{2}}{{\tan }^{-1}}\frac{x}{y}$, then $\frac{{{\partial }^{2}}u}{\partial x\,\partial \,y}=$
	If ${{u}^{2}}={{(x-a)}^{2}}+{{(y-b)}^{2}}+{{(z-c)}^{2}}$, then $\sum \frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}=$
	If $z=\sec \,(y-ax)+\tan (y+ax),$ then $\frac{{{\partial }^{2}}z}{\partial {{x}^{2}}}-{{a}^{2}}\frac{{{\partial }^{2}}z}{\partial {{y}^{2}}}=$
	If $z=\frac{y}{x}\left[ \sin \frac{x}{y}+\cos \left( 1+\frac{y}{x} \right) \right]$, then $x\frac{\partial z}{\partial x}=$
	If $u={{e}^{-{{x}^{2}}-{{y}^{2}}}}$, then