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An Extension of the Arithmetic Derivative

By Seung Jae Lee V Form, Alex Padron VI Form, and Luya Wang VI Form

Instructor:  Mr. Rick Umiker, Mathematics Faculty

Abstract:  In this paper, we examine the product rule and the arithmetic derivative. We first find a closed-form formula for the arithmetic derivative over positive integers. We then extend the argument to negative numbers, rational numbers, power roots, and complex numbers. Throughout our research, we also use Mathematica graphics to help visualize the behavior of the arithmetic derivative over different domains and explore boundary conditions and intermediate lines. Finally, we discuss the continuity of arithmetic derivative and give a continuous form that satisfies the product rule.Please click on this link to an accessible Google doc to read the paper, including equations, graphs, images, and data charts:

An Extension of the Arithmetic Derivative

Seung Jae (Ryan) Lee is a V Former from Seoul, Korea, and he lives in Sawyer House.  He is passionate about math and computer science, and he often writes a post in his blog on math and computer science. 

Alex Padron is a VI Former who lives in Sawyer House.  He is from Sherman, CT. Alex has a passion for math and science, and he and his partner went undefeated in 2013 in JV tennis doubles matches. 

Luya Wang, VI Form, is from Hangzhou, China.  In addition to being a scientist, Luya partakes in studio art, plays softball, and reads classics such as Crime and Punishment.

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