Arithmetic derivative intuition
$begingroup$
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
363313
$endgroup$
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
363313
$endgroup$
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 |
$begingroup$
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
363313
$endgroup$
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
363313
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
363313
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
363313
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
363313
asked Dec 28 '18 at 21:57
Benjamin ThoburnBenjamin Thoburn
363313
363313
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 |
0
active
oldest
votes
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055329%2farithmetic-derivative-intuition%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3055329%2farithmetic-derivative-intuition%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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