what does it mean when a partial derivative has a prime on it? usually i just see partial derivatives as f and a subscript x but i recently came across f with a subscript x and a prime on the top. just curious, what does that mean?
One possibility: f is a function of position and time (so it is a physics problem) and they are using the ' to distinguish differentiation with respect to time, t, while using the partial derivative to indicate differentiation with respect to a space variable.
Another possibility: there are (at least) two different "f" functions, one called f and the other called f' and the prime is used only to distinguish functions.
Which, if either, of those is correct would depend on the context.