In the case, "x" is just another variable like "u" or "v". However we gave "x" specific terms, x = 1.
So you're saying that you derive f(x) = x and then plug in 1? No. You have to plug in the 1 first, and then derive, and the answer is 0.
Look up this problem online, I'm sure you can find it on wikipedia or something. It'll explain it for you.