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
It’s actually extremely useful in specific areas. If you have an expression like the above, it can represent the amount or state of something. If you take its derivative, you get an expression for the rate (and direction) of the *change* of that state or amount. You can actually make some important inferences on systems (represented by functions/expressions) or variables simply by looking at its derivative.
It only seems random because you’re being given functions that are made out of thin air, so what they represent is meaningless, and the process of knowing how to take a derivative is their only point to exist.
Latest Answers