What does the equation in the attached file mean in the f ' (x) notation?
vv' = (v2)'/2
In Lagrange's notation f'(x), please, as I asked?
They also say there: "In steady flow u=u(x), so..."...so the equation I asked about. What do they mean? How can it not be that u=u(x)?
When you write u=u(x) you're simply clarifying that the function is dependent on x. It's very common to just stop writing u(x) because everybody knows that it's a function of x (for example, epenguin's post)
v' is v'(x) in epenguin's post, and v is v(x) so it's v(x)v'(x)=(v(x)2)'/2
Separate names with a comma.