Derivative is one of my favorite concepts; it is the fundamental idea of calculus.
Derivative represents the rate of instantaneous change at the point a.
Math started to make sense to me systematically from calculus.
One application is
S'(t) = v(t) : velocity
S”(t)= v'(t)= a(t): accerlation
and dont forget S”'(t)= jerk 🙂