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Spiritual_Jaguar4685 t1_iy83c7j wrote

Calculus was "invented" roughly at the same time by two different people, using it for two different purposes.

Isaac Newton used it as a solution to physics problems, and Leibniz (not sure his first name) used it for more pure math problems.

At its heart they were both concerned with being able to calculate the slope of a line at possible point on the line (if you imagine a straight line that's easy, but a constantly changing wiggly curvy line is hard).

Both people realized that a slope on a line is just rise over run or change in Y divided change in X on a graph. And both people created a math process to make the "change" values infinitely small giving a new equation, this process is called a "transformation" (derivation in this case).

Where they differed is that Newton was more concerned real world physics, he was mostly interested with changes in a system by time very specifically where as Leibniz was more pure-math focused and just wanted to discover what are essentially "tangents" (point-slopes) on curves.

From Leibniz we get the dY/dX notations and from Newton we get the y' and x' notation which (In my engineering school at least) specifically refers to time-based derivates.

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left_lane_camper t1_iy9bfw4 wrote

>From ... Newton we get the y' and x' notation which (In my engineering school at least) specifically refers to time-based derivates.

Interesting! We used a prime for spatial derivatives and a tittle for time derivatives in my physics education when we used Newtonian notation.

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Spiritual_Jaguar4685 t1_iy9bn3a wrote

I could be misremembering... this was quite a bit ago.

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left_lane_camper t1_iy9c2nw wrote

It doesn't seem unreasonable that we could have used the notation differently as well. There's no fundamental reason why a prime has to be a space derivative and a tittle a time derivative. It might make communication a little tricky at first, but the meaning should be made clear by context (and if it isn't, we probably would want to use more specific notation anyway).

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Spiritual_Jaguar4685 t1_iy9d05i wrote

Well you got me remembering now.

I think we used "X-dot" (X with a tittle) specifically for velocity as x represented physical distance/displacement and X-dot-dot for acceleration.

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