A high IQ person, like Kalid, can figure it out himself.

The derivative is the division of a subtraction and integration is the addition of a multiplication

Alternatively, the derivative is ‘instantaneous division’ and integration is the accumulation of infinite instantaneous multiplications.

Hope that’s right. :/

‘we need an instrument of some kind to make a measurement, but we need to remember that the instrument itself can affect the outcome, so we get a better instrument such that the effect on the reading we get is negligible by our own instrument’s standards of accuracy.’

‘….So, if you like, dx (or dt) is an artificial measurement we introduce in order to get a model, then we make it perfect by pretending dx was never there.’

Or is it the case, conversely, borrowing from your ‘Why Do We Need Limits and Infinitesimals’ discussion, is dx (or dt) a ‘more accurate measurement’ we introduce at a higher level of resolution, in order to measure the rate of change of something, and which we then can treat as zero when bringing the result back into our standard measure of accuracy (no matter what measure of accuracy we happen first to pick)?

In other words, we are always taking measurements with imprecise tools, but dx (or dt) is a slightly better tool then the one we have, such that we can treat its effect on the patient as zero.

Imagine some old school horrible instrument used in medicine versus today’s slightly less hellish instruments – by the standard of the past, today’s instruments have negligible impact on the patient’s heart rate readings.