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

Something of a nitpick: This doesn’t apply to all functions, only functions of the form ax^b where b isn’t 0. As others have said, you can show that it is the case from the definition of a derivative, but it is not itself really anything special.