If $u \equiv u(x, y) = \sin(y + ax) - (y + ax)^2$,then it implies

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 $u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)$, then the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is

If $u = \tan^{-1}(\frac{y}{x})$,then by Euler's Theorem,the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is:

If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$,then $(x+y+z)(u_x+u_y+u_z)$ is equal to

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} = $