df/dx is actually completely obvious. It tells you exactly what's going on, since df is the change of f and dx is the change of x, for very small changes. It's

df/dx is actually completely obvious. It tells you exactly what's going on, since df is the change of f and dx is the change of x, for very small changes. It's a lot more precise than simply writing f'. Newton wrote a dot over f and a lot of physicists still do that.