Understanding the Equation in f'(x) Notation

[luckis11]

What does the equation in the attached file mean in the f ' (x) notation?

 

[epenguin]

vv' = (v²)'/2

 

[luckis11]

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)?

http://en.wikipedia.org/wiki/Bernoulli's_equation#Derivations_of_Bernoulli_equation

 

[Office_Shredder]

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