> the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only

> the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? Because higher derivatives are insignificant. That's the entire concept of Taylor series approximation. If you change a high derivative of a function, the value of the function won't noticeably change - why would you care?