Reading the Signs

A positive derivative means the quantity is increasing. A negative derivative means it is decreasing. Zero means it has paused, at least for that instant. Watching how the derivative itself changes reveals acceleration — the derivative of the derivative.

This layering is powerful. Position gives location. Its first derivative gives velocity. The second derivative gives acceleration. The third — called jerk — describes how sharply acceleration changes. Every smooth physical motion can be described by stacking derivatives.