for $f:\mathbb{R}^{2}\to\mathbb{R}$ I have to transform the expression $\frac{\partial^{2}f}{\partial x^{2}}$ to the coordinates $u=x^{2}+2xy, v=x^{2}+2xy$.
I know that I can write $\frac{\partial f}{\partial x}=\frac{\partial f}{\partial u}\frac{\partial u}{\partial x}+\frac{\partial f}{\partial v}\frac{\partial v}{\partial x}$ but the problem is that if I want to write $\frac{\partial u}{\partial x}$ and $\frac{\partial v}{\partial x}$ in terms of $u$ and $v$ then I'd have to solve for $x$ and $y$ in the equations above but I think it,s not possible. Do you have any sugestions?
