Re: "what is the deriative actually?"

Just to add another option, I'm used to use simple physics concepts to
explain people what derivatives are. A good example is the equation d
= d0 + v.t (distance equals velocity times time). Obviously the
position d of an arbitrary object can be determined in terms of t by
any kind of function, I'm just using a linear approach here because
it's secondary level and most people seem to understand it. In short:
think of the velocity as a constant in this case, please, and consider
that we are just defining d in terms of t (d = f(t)).

Using the Leibniz's notation, the derivative can be clearly
represented by dd/dt, where dt is an infinitesimal increase in t and
dd is the increase in distance associated. Thus, the quotient
represents the RATE in which distance grows across time for a certain
model. In this case, the derivative dd/dt is obviously the constant v
for any point. For any function, though, the derivative at a certain
point is called instantaneous speed, which can be easily understood by
"non-math" people using the analogy of a car's speedometer.

You might want to read a little about Leibniz's Notation, maybe it
happens yourself to get a better understand of what not only
derivatives, but calculus itself is all about:

http://en.wikipedia.org/wiki/Leibniz's_notation
.

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