Re:On Leibniz Notation
by galaxyLogic on Saturday January 20, 2024 @03:50AM
(#39065796)
A simple conceptual description of a derivative is "speed".
To measure the speed of a moving object you must divide the distance moved by the time it took to move that distance.
So how can you measure what the speed is at a given location? In a sense you cannot, you can only measure it at a given interval over the period of time it took to move that distance.
So it is kind of confusing. dx/dy represents the limit of measuring the speed over increasingly small distances and durations around a given point in space and time. If you take dx to 0 and dy to 0 it does not make sense because 0/0 is ill-defined. Therefore we need some notation that implies we are really not talking about a single point, but an increasingly small distance, and duration.
To measure the speed of a moving object you must divide the distance moved by the time it took to move that distance.
So how can you measure what the speed is at a given location? In a sense you cannot, you can only measure it at a given interval over the period of time it took to move that distance.
So it is kind of confusing. dx/dy represents the limit of measuring the speed over increasingly small distances and durations around a given point in space and time. If you take dx to 0 and dy to 0 it does not make sense because 0/0 is ill-defined. Therefore we need some notation that implies we are really not talking about a single point, but an increasingly small distance, and duration.