Ioannis,
Really, I think we are basicly saying the same thing here, however.... You wrote:
Well the derivative is a number (no units associated with).
I think this is where you are wrong. The derivative is the rate of change. But you cant just say that the rate of change is 7. You have to say 7 this per that otherwise it doensn't make sense IMO. For example 1.5V per second or 25degrees per hour or 15m/s per second etc.

I found this on Wikipedia:
In mathematics, a derivative is the rate of change of a quantity. A derivative is an instantaneous rate of change: it is calculated at a specific instant rather than as an average over time. The process of finding a derivative is called differentiation. The reverse process is integration. The two processes are the central concepts of calculus and the relationship between them is the fundamental theorem of calculus.
Again, I believe we're meaning the same thing but without assigning units to the numbers they just doesn't make sense.

/Henrik Olsson.