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
A function shows the value of something at certain parameters.
A derivative of a function shows the rate of change for that function in respect to a certain parameter (Time, for example). An integral shows the sum of the function in respect to a certain parameter (again, like Time).
A simpler example is if you have a function that describes the position of something, then the derivative of this function would be the rate of change in **position**. Rate of change of position? That’s **speed**. Suddenly, you have a function that describes the speed.
If you derive this function of speed, now you get the rate of change in speed. That just means **acceleration**.
Derivative (and Integral) is incredibly useful and is sometimes the basis of certain smaller fields, from robotic control systems, to stock market exchanges.
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