How come reducing the power of a function by 1 and multiplying the function by it gives us derivative of the function?

Question

Is it just a coincidence, or is it like an assumption and everything else is built around it?

In: 0

Answer 1

In mathematics concepts can be defined in many ways: we like to talk about equivalent characterizations. For example the exponential function has [6 equivalent characterizations](https://en.wikipedia.org/wiki/Characterizations_of_the_exponential_function). Note that the derivative of the exponential function is itself hence your assumption doesn’t hold here.