# 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 |
---|---|

Canonical name | ExampleOfArithmeticDerivative |

Date of creation | 2013-03-22 13:35:12 |

Last modified on | 2013-03-22 13:35:12 |

Owner | Johan (1032) |

Last modified by | Johan (1032) |

Numerical id | 7 |

Author | Johan (1032) |

Entry type | Example |

Classification | msc 11Z05 |