Because that's the way it works when one differentiates a function with two unknowns. You kind of need to acknowledge the fact that you're differentiating the function with respect to x, not to u. So, when you have u, you can't just write "du", you need to add this /dx. Technically speaking, this is not a fraction, but it does behave as one.
Nope, I'm glad if I'm of any help)