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
In physics you use derivatives all the time. Speed is derivative of position over time, acceleration is derivative of speed over time.
With derivative you can have a simple test of smaller or greater than 0 to see if derived function is increasing or decreasing. Derivative can be used to find local minimum and maximum of a function which has use in optimisation problems.
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