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
Derivative function measure the rate of change of something. Which is useful in many areas.
An object acceleration is the change rate of its speed. That’s a derivative.
It also ties correlated items that change together.
If you have to pay a booking fee for something, the fee changes following the price changes of the underlying item you want to buy. That’s a derivative too. (Example taken from financial options).
If the derivative equals 0, there is no change to the vertical axis when the horizontal axis change.
If the derivative equals X, one increment on the horizontal axis will cause X increments on the vertical axis.
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