Suppose I get the an equation like
$$ \frac{ds(t)}{dt} = \sum_i \frac{ds_i(t)}{dt} ,$$
as the result of some computation. In order to simplify this further I invoke the notion of the differential whereby $ds=s'(t)\, dt$ and multiply the whole equation with $dt$ to arrive at
$$ ds = \sum_i ds_i\,. $$
While this looks simpler and in particular looks like it is independent of $t$, I wonder whether this is rather self deception, or whether this is indeed a meaningful simplification because the $t$, as a free parameter, plays only a technical role that need not necessarily be shown.
Does the answer depend on the meaning of the $s$ and the $s_i$. For example does it make a difference if the $s_i$ are points in space.