In Leibniz notation, how do you write the second derivative of y with respect to the square of x?
$begingroup$
I know how to write in Leibniz notation for more plain-vanilla expressions like the the second derivative of y with respect to x. But I am not sure how to write, in Leibniz notation, the second derivative of y with respect to expressions more complex than a single variable. In, for example, the second derivative of y with respect to the square of x, would I just use parentheses and write $dy^2/d(x^2)^2$?
calculus derivatives notation
edited Jan 7 at 18:50
gt6989b
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I know how to write in Leibniz notation for more plain-vanilla expressions like the the second derivative of y with respect to x. But I am not sure how to write, in Leibniz notation, the second derivative of y with respect to expressions more complex than a single variable. In, for example, the second derivative of y with respect to the square of x, would I just use parentheses and write $dy^2/d(x^2)^2$?
calculus derivatives notation
edited Jan 7 at 18:50
gt6989b
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50
add a comment |
$begingroup$
I know how to write in Leibniz notation for more plain-vanilla expressions like the the second derivative of y with respect to x. But I am not sure how to write, in Leibniz notation, the second derivative of y with respect to expressions more complex than a single variable. In, for example, the second derivative of y with respect to the square of x, would I just use parentheses and write $dy^2/d(x^2)^2$?
calculus derivatives notation
edited Jan 7 at 18:50
gt6989b
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I know how to write in Leibniz notation for more plain-vanilla expressions like the the second derivative of y with respect to x. But I am not sure how to write, in Leibniz notation, the second derivative of y with respect to expressions more complex than a single variable. In, for example, the second derivative of y with respect to the square of x, would I just use parentheses and write $dy^2/d(x^2)^2$?
calculus derivatives notation
calculus derivatives notation
edited Jan 7 at 18:50
gt6989b
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 7 at 18:50
gt6989b
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 7 at 18:50
gt6989b
33.4k22452
edited Jan 7 at 18:50
gt6989b
33.4k22452
edited Jan 7 at 18:50
gt6989b
33.4k22452
33.4k22452
asked Jan 7 at 18:48
resplaineresplaine
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 7 at 18:48
resplaineresplaine
61
asked Jan 7 at 18:48
resplaineresplaine
61
61
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
resplaine is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50
add a comment |
1
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50
1
1
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Indeed, if $z=x^2$ and you need
$$
frac{d^2y}{dz^2} = frac{d^2 y}{dleft(x^2right)^2}
$$
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
$endgroup$
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
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
});
}
});
resplaine is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3065343%2fin-leibniz-notation-how-do-you-write-the-second-derivative-of-y-with-respect-to%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Indeed, if $z=x^2$ and you need
$$
frac{d^2y}{dz^2} = frac{d^2 y}{dleft(x^2right)^2}
$$
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
$endgroup$
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
add a comment |
$begingroup$
Indeed, if $z=x^2$ and you need
$$
frac{d^2y}{dz^2} = frac{d^2 y}{dleft(x^2right)^2}
$$
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
$endgroup$
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
add a comment |
$begingroup$
Indeed, if $z=x^2$ and you need
$$
frac{d^2y}{dz^2} = frac{d^2 y}{dleft(x^2right)^2}
$$
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
$endgroup$
Indeed, if $z=x^2$ and you need
$$
frac{d^2y}{dz^2} = frac{d^2 y}{dleft(x^2right)^2}
$$
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
answered Jan 7 at 18:50
gt6989bgt6989b
33.4k22452
33.4k22452
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
add a comment |
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
$begingroup$
Thanks so much! That's just the answer I needed.
$endgroup$
– resplaine
Jan 7 at 18:58
add a comment |
resplaine is a new contributor. Be nice, and check out our Code of Conduct.
resplaine is a new contributor. Be nice, and check out our Code of Conduct.
resplaine is a new contributor. Be nice, and check out our Code of Conduct.
resplaine is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3065343%2fin-leibniz-notation-how-do-you-write-the-second-derivative-of-y-with-respect-to%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
$begingroup$
It’s $d^2y$, not $dy^2$.
$endgroup$
– KM101
Jan 7 at 18:50