Math Idea – Derivative similarity

My idea is simple.

Inspired by e^x where the derivative is equal to e^x. I cold guess that maybe there should exist something like ’derivative similarity’.

So I will test a machine learning approach to this. I will start with some function and take the derivative of it. Place 2 derivatives and the function in separate series. Label the samples coming from f,df,df2.

After learning the function and its first and second derivative I will If I’m successful see what happens when I try to maximize prob[0]+prob[2]. That I want to see if there is a function that has a second derivative but no first derivative. Sounds crazy. Probably is. : ).

Well I think there is a lot to be tested with machine learning.

Here I calculated something that maybe can be called continous derivate. Ex. D(.25)(f(x))