If $u = u(x, y) = \sin(y + ax) - (y + ax)^2$,then which of the following is true?

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 $u = x y^2 \tan^{-1}\left(\frac{y}{x}\right)$,then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to

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 $z = \sec^{-1}\left(\frac{x^4+y^4-8x^2y^2}{x^2+y^2}\right)$,then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ 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} = $