Let $A = (\frac{\partial{z}}{\partial{x}})^2 + (\frac{\partial{z}}{\partial{y}})^2$. Transfer $A$ when considering $x$ as a function and $u = xz$ and $v = yz$ as independent variables.
It is an exercise practicing for my test that my teacher gave me. At first $z = z(x, y)$ and we must transfer to a new expression where $x=x(u, v)$ where $u, v$ are defined as above. At first I think that the problem is incorrect, but it's not. My teacher gave us something kind of clues but I can't do anything more: $u = xz$ and then derivative both sides in term of $u$, we get $1 = \frac{\partial{x}}{\partial{u}}.z + \frac{\partial{z}}{\partial{u}}.x$