Question

Is this derivative rule correct?

The derivative of speed is velocity
Derivative of velocity is acceleration

Where does area fit in?

Answer 1

if you are taking the derivative with respect to time and your units are consistent , th rule is perfectly correct,
the area under the curve is integral (the area under the acceleration curve is equal to the velocity
and the area under the velocity cure is the total area displaced

Answer 2

Oh okay I see. Now, is it speed or position that has a derivative of velocity ?

Answer 3

\[\frac{\text d x} {\text d t}=\dot x=v\]\[\frac{\text d^2 x} {\text d t^2}=\frac{\text d v} {\text d t}=\ddot x=a\]

Answer 4

thank you unklerhaukus