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

 

[blue_raver22]

In f'(x) notation, the equation in the attached file represents the derivative of the function f(x). This means that the equation is showing the rate of change of the function f(x) at a specific point x. The notation f'(x) is read as "f prime of x" and it represents the slope of the tangent line to the graph of f(x) at the point x. It is a fundamental concept in calculus and is used to analyze the behavior of functions and their rates of change. By understanding the equation in f'(x) notation, we can gain insights into the behavior of the function and make predictions about its future values.