# example of arithmetic derivative

Consider the natural number $6$. Using the rules of the arithmetic derivative we get:
$6^{\prime}=(2\cdot 3)^{\prime}=2^{\prime}\cdot 3+2\cdot 3^{\prime}=1\cdot 3+2% \cdot 1=5$

Below is a list of the 10 first natural numbers and their first and second arithmetic derivatives:
$n$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $n^{\prime}$ $0$ $1$ $1$ $4$ $1$ $5$ $1$ $12$ $6$ $7$ $n^{\prime\prime}$ $0$ $0$ $0$ $4$ $0$ $1$ $0$ $16$ $5$ $1$

Title example of arithmetic derivative ExampleOfArithmeticDerivative 2013-03-22 13:35:12 2013-03-22 13:35:12 Johan (1032) Johan (1032) 7 Johan (1032) Example msc 11Z05