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
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.
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