If $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$,then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to

If $F(u) = f(x, y, z)$ is 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 $u = (x^2 + y^2 + z^2)^{3/2}$,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 $z = \frac{y}{x} \left[ \sin \frac{x}{y} + \cos \left( 1 + \frac{y}{x} \right) \right]$, then $x \frac{\partial z}{\partial x}$ is equal to

If $z = \frac{(x^4 + y^4)^{1/3}}{(x^3 + y^3)^{1/4}}$,then $x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y} = $

If $z = \frac{y}{x} \left[ \sin \left( \frac{x}{y} \right) + \cos \left( 1 + \frac{y}{x} \right) \right]$,then $x \frac{\partial z}{\partial x} = $