Questions in differentiation

Select	Question
	If $z={{\tan }^{-1}}\left( \frac{x}{y} \right)$, then ${{z}_{x}}:{{z}_{y}}=$
	If $u=\frac{x+y}{x-y}$, then $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=$
	If $u=\log ({{x}^{2}}+{{y}^{2}}),$ then $\frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}=$
	If $u={{\sin }^{-1}}\left( \frac{y}{x} \right),$ then $\frac{\partial u}{\partial x}$ is equal to
	If $u={{\tan }^{-1}}\frac{y}{x}$, then by Euler’s Theorem the value of x $\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=$
	If $u={{\tan }^{-1}}\left( \frac{{{x}^{3}}+{{y}^{3}}}{x-y} \right)$, then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=$
	If $F(u)=f(x,\,y,\,z)$ be a homogeneous function of degree $n$ in $x,\,y,\,z$ then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}+z\frac{\partial u}{\partial z}=$
	If $u=\log ({{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz)$, then $\left( \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} \right)$ $(x+y+z)$ =
	If $z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)$, then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}$ is equal to
	If $u={{\log }_{e}}({{x}^{2}}+{{y}^{2}})+{{\tan }^{-1}}\left( \frac{y}{x} \right)$, then $\frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}=$