I just came across this idea of a number derivative and wondered about applications or interesting diagrams. Wikipedia has this to say: https://en.wikipedia.org/wiki/Arithmetic_derivative.
Additional information
The Arithmetic Derivative is not the standard derivative one learns in calculus. Here is a definition and some examples:
http://planet2.math.uwaterloo.ca/arithmeticderivative
The arithmetic derivative n′ of a natural number n is defined by the following rules:
- p′=1 for any prime p.
- (ab)′=a′b + ab′ for any a, b ∈ N (Leibniz rule).
0'=0
1'=0
2'=1
96'=272
p'=1, if p is prime
Good Question. Follow the link to know more: https://www.quora.com/How-is-standard-deviation-used-in-the-real-world
Arithmetic derivative. In number theory, the Lagarias arithmetic derivative, or number derivative, is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis.
Arithmetic derivative - Wikipedia
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