Calculus
posted by Ralph .
What is the difference between f'(x), y', and dy/dx?

Just notation.
they mean the same thing.
I say tomato, you say "tomaato" 
If y is the dependent variable and x the independent variable, they are all the same.
The minor syntaxical differences are
1. in f'(x), the variable y is not necessary, as f(x) takes the place of y.
2. in y' (Newton's notation), the independent variable is understood according to context. If there is no other information, it would probably be x.
3. dy/dx (Leibniz notation) This is the explicit form with no ambiguities.