The formula for the second derivative of distance with respect to time is

$a = \dfrac{d}{dt}\left(\dfrac{ds}{dt}\right)$

$= \dfrac{d^2s}{dt^2}$ (just the $t$ is squared - it's not $dt$ all squared).

The question is why is $dt$ multiplied by $dt$ equal to $dt^2$ with just the $t$ squared. Why is not the $d$ also squared? As we can see $d . ds$ becomes $d^2 s$.

Apologies for this probably simple question, I am at the beginning of a very long road in maths.