I am given $u=\frac{x+y}{\sqrt 2}$ and $v=\frac{x-y}{\sqrt2}$, how would I find $\frac{d^2}{du^2},\frac{d^2}{dv^2}$?
I rearranged $u$ and $v$ in terms of $x$ and $y$, and I get $x = \frac{u + v}{\sqrt{2}}$ and $y = \frac{u - v}{\sqrt{2}}$. But how do I find $\frac{d^2}{du^2}$ and $\frac{d^2}{dv^2}$?