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Reference.org
Arithmetic derivative
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<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, the Lagarias arithmetic derivative or number derivative is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> defined for <a href="/facts/Integer/PUwwrawx">integers</a>, based on <a href="/facts/Prime_factorization/EjMCTz2t">prime factorization</a>, by analogy with the <a href="/facts/Product_rule/MyKxsP5t">product rule</a> for the <a href="/facts/Derivative/7Ito70Dh">derivative of a function</a> that is used in <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a>. </p><p>There are many versions of "arithmetic derivatives", including the one discussed in this article (the Lagarias arithmetic derivative), such as Ihara's arithmetic derivative and Buium's arithmetic derivatives. </p>