I don’t mean in which cases I can use them, nor how they work. I know how they work (at least at a basic level, the derivative of ax\^b is abx\^(b-1), but I mean… why is a function that does those steps useful to solve any problem? It really seems like a random choice of operations.
In: Mathematics
I wish they taught modeling in high schools. It would help immensely with this type of confusion.
If F(x) tells you how much of something there is then its derivative F'(x) tells you how quickly that changes. You can do this multiple times to track how the layer below changes.
This is useful.
Example: speed does not kill you, but a sudden change in speed will. Calculating the acceleration derivative for something like a roller coaster will help you not kill people riding it.
Physics is just math applied to the real world. Many things in this world can be “modeled” by relatively simple math equations. However, while we can use different terms to represent different things, those things we are representing still exist in the real world, and in the real world things don’t happen at the snap of a finger.
At the very end of the day it’s a bunch of atoms hitting each other or being influenced by some energy waves, derivatives allow us to closer model the realest state of the universe
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