Arithmetic derivative intuition
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Is there a reason for defining the arithmetic derivative of a prime as 1, ie what intuition about normal derivatives makes us define this property in particular, or how did this name appear (that is more secondary/optional however, otherwise I would've posted this on history of math and science, but if helps to answer the question...).
I may or may not then be able to understand why the product rule, as opposed to something else, is carried over (probably because of how products relate to primes), which is also a bit of mystery. What I've said here is the entirety of my knowledge of arithmetic derivatives and I'm not learning this in a class so I don't know how this relates to other math. Thanks in advance.
number-theory derivatives
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
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add a comment |
$begingroup$
Is there a reason for defining the arithmetic derivative of a prime as 1, ie what intuition about normal derivatives makes us define this property in particular, or how did this name appear (that is more secondary/optional however, otherwise I would've posted this on history of math and science, but if helps to answer the question...).
I may or may not then be able to understand why the product rule, as opposed to something else, is carried over (probably because of how products relate to primes), which is also a bit of mystery. What I've said here is the entirety of my knowledge of arithmetic derivatives and I'm not learning this in a class so I don't know how this relates to other math. Thanks in advance.
number-theory derivatives
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
$endgroup$
1
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I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
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– Noble Mushtak
Dec 28 '18 at 22:19
add a comment |
$begingroup$
Is there a reason for defining the arithmetic derivative of a prime as 1, ie what intuition about normal derivatives makes us define this property in particular, or how did this name appear (that is more secondary/optional however, otherwise I would've posted this on history of math and science, but if helps to answer the question...).
I may or may not then be able to understand why the product rule, as opposed to something else, is carried over (probably because of how products relate to primes), which is also a bit of mystery. What I've said here is the entirety of my knowledge of arithmetic derivatives and I'm not learning this in a class so I don't know how this relates to other math. Thanks in advance.
number-theory derivatives
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
$endgroup$
Is there a reason for defining the arithmetic derivative of a prime as 1, ie what intuition about normal derivatives makes us define this property in particular, or how did this name appear (that is more secondary/optional however, otherwise I would've posted this on history of math and science, but if helps to answer the question...).
I may or may not then be able to understand why the product rule, as opposed to something else, is carried over (probably because of how products relate to primes), which is also a bit of mystery. What I've said here is the entirety of my knowledge of arithmetic derivatives and I'm not learning this in a class so I don't know how this relates to other math. Thanks in advance.
number-theory derivatives
number-theory derivatives
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
350213
350213
1
$begingroup$
I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
$endgroup$
– Noble Mushtak
Dec 28 '18 at 22:19
add a comment |
1
$begingroup$
I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
$endgroup$
– Noble Mushtak
Dec 28 '18 at 22:19
1
1
$begingroup$
I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
$endgroup$
– Noble Mushtak
Dec 28 '18 at 22:19
$begingroup$
I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
$endgroup$
– Noble Mushtak
Dec 28 '18 at 22:19
add a comment |
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$begingroup$
I think this article might help you: math.arizona.edu/~ura-reports/063/Sandhu.Aliana/Final.pdf
$endgroup$
– Noble Mushtak
Dec 28 '18 at 22:19