This is correct.

Actually, it IS correct but do you understand why? You cannot just say the partial derivatives are 0 because the value of the function is 0. In order to calculate or , you have toSecond case:

If

varyx while holding y constant and vice-versa. Youcannothave "y= -x" for every such point.

You need to use

and

Is this right? I would like to know why it isn't, I think its not. Should I think when I consider the second case as I would go in all directions or something like that? cause in other cases where I got defined different functions for a particular point I've used the definition, but in this case I got trajectories. What should I do?

Bye and thanks.