Issue in applying partial chain rule
$begingroup$
I was reading through a derivation and saw this
I think it's using the partial derivative chain rule but I'm not sure how it's being applied in this case. Any ideas? We always used to do this little tree diagrams to solve the partial derivatives but not sure how to go about that here.
derivatives partial-derivative
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
$endgroup$
add a comment |
$begingroup$
I was reading through a derivation and saw this
I think it's using the partial derivative chain rule but I'm not sure how it's being applied in this case. Any ideas? We always used to do this little tree diagrams to solve the partial derivatives but not sure how to go about that here.
derivatives partial-derivative
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
$endgroup$
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48
add a comment |
$begingroup$
I was reading through a derivation and saw this
I think it's using the partial derivative chain rule but I'm not sure how it's being applied in this case. Any ideas? We always used to do this little tree diagrams to solve the partial derivatives but not sure how to go about that here.
derivatives partial-derivative
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
$endgroup$
I was reading through a derivation and saw this
I think it's using the partial derivative chain rule but I'm not sure how it's being applied in this case. Any ideas? We always used to do this little tree diagrams to solve the partial derivatives but not sure how to go about that here.
derivatives partial-derivative
derivatives partial-derivative
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
asked Dec 2 '18 at 0:49
AlfroJang80AlfroJang80
1483
1483
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48
add a comment |
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48
add a comment |
0
active
oldest
votes
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
});
}
});
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%2f3022075%2fissue-in-applying-partial-chain-rule%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%2f3022075%2fissue-in-applying-partial-chain-rule%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
$begingroup$
This looks relevant: math.stackexchange.com/questions/217702/…. If you exchange the derivative and expectation, you can get your result very easily. The question really is whether the conditions under which the interchange is valid hold in your case.
$endgroup$
– Aditya Dua
Dec 2 '18 at 3:48