If $u(x, y)=y \log x+x \log y$,then $u_x u_y-u_x \log x-u_y \log y+\log x \log y$ is equal to :

If $u = x^2 + y^2$ and $x = s + 3t, y = 2s - t,$ then $\frac{d^2u}{ds^2} = $

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

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 $F(u) = f(x, y, z)$ 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 ${x^x}{y^y}{z^z} = c$,then ${{\partial z} \over {\partial x}} = $