If $x+y^2=u, y+z^2=v, z+x^2=w$ find $\frac{\partial x}{\partial u}, \frac{\partial^2 x}{\partial^2 u}, \frac{\partial^2 x}{\partial u \partial v}$
I've found out the first one using jacobians, but I have no idea of solving others. How should I approach?