i do not say they are independent. y(x) and x are not indepentent either, still in a partial derivative of z with respect to x, one does not consider the y(x).
so orodruin, i see that they are related by the metric. y(x) is also related to x by its defining function. so i do still not get the...
i have a mathematical question which is quite similar to one asked before, still a bit different
https://www.physicsforums.com/threads/derivative-of-first-term-in-lagrangian-density-for-real-k-g-theory.781472/the first term of KG-Lagrangian is: \frac{1}{2}(\partial^{\mu} \phi)(\partial_{\mu}...