How to determine the $dy$-term of the differential of $f(x,y,z)= sin(x+y)sin(y+z)$ to be $sin(x+2y+z)$?
$begingroup$
So I want to know how I can simplify the $dy$-part of the differential of $f(x,y,z)= sin(x+y)sin(y+z)$.
I already have the $dx$-term which is $[cos(x+y)sin(y+z)]dx$ and the $dz$-term which becomes $[sin(x+y)sin(y+z)]dz$.
So I already know that the differential of the entire thing is
$df(x,y,z)= [cos(x+y)sin(y+z)]dx+ sin(x+2y+z)dy + [sin(x+y)cos(y+z)]dz$
The question actually is what is the $dfrac{partial f(x,y,z)}{partial y}$? I don't know any trigonemetric identity to of 3 terms into 1 sin. Can someone explain this to me?
EDIT: I already have for the $dy$-term that $cos(x+y)sin(y+z)+ cos(y+z)sin(x+y)]dy$
calculus derivatives partial-derivative
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
$endgroup$
add a comment |
$begingroup$
So I want to know how I can simplify the $dy$-part of the differential of $f(x,y,z)= sin(x+y)sin(y+z)$.
I already have the $dx$-term which is $[cos(x+y)sin(y+z)]dx$ and the $dz$-term which becomes $[sin(x+y)sin(y+z)]dz$.
So I already know that the differential of the entire thing is
$df(x,y,z)= [cos(x+y)sin(y+z)]dx+ sin(x+2y+z)dy + [sin(x+y)cos(y+z)]dz$
The question actually is what is the $dfrac{partial f(x,y,z)}{partial y}$? I don't know any trigonemetric identity to of 3 terms into 1 sin. Can someone explain this to me?
EDIT: I already have for the $dy$-term that $cos(x+y)sin(y+z)+ cos(y+z)sin(x+y)]dy$
calculus derivatives partial-derivative
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
$endgroup$
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48
add a comment |
$begingroup$
So I want to know how I can simplify the $dy$-part of the differential of $f(x,y,z)= sin(x+y)sin(y+z)$.
I already have the $dx$-term which is $[cos(x+y)sin(y+z)]dx$ and the $dz$-term which becomes $[sin(x+y)sin(y+z)]dz$.
So I already know that the differential of the entire thing is
$df(x,y,z)= [cos(x+y)sin(y+z)]dx+ sin(x+2y+z)dy + [sin(x+y)cos(y+z)]dz$
The question actually is what is the $dfrac{partial f(x,y,z)}{partial y}$? I don't know any trigonemetric identity to of 3 terms into 1 sin. Can someone explain this to me?
EDIT: I already have for the $dy$-term that $cos(x+y)sin(y+z)+ cos(y+z)sin(x+y)]dy$
calculus derivatives partial-derivative
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
$endgroup$
So I want to know how I can simplify the $dy$-part of the differential of $f(x,y,z)= sin(x+y)sin(y+z)$.
I already have the $dx$-term which is $[cos(x+y)sin(y+z)]dx$ and the $dz$-term which becomes $[sin(x+y)sin(y+z)]dz$.
So I already know that the differential of the entire thing is
$df(x,y,z)= [cos(x+y)sin(y+z)]dx+ sin(x+2y+z)dy + [sin(x+y)cos(y+z)]dz$
The question actually is what is the $dfrac{partial f(x,y,z)}{partial y}$? I don't know any trigonemetric identity to of 3 terms into 1 sin. Can someone explain this to me?
EDIT: I already have for the $dy$-term that $cos(x+y)sin(y+z)+ cos(y+z)sin(x+y)]dy$
calculus derivatives partial-derivative
calculus derivatives partial-derivative
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
edited Dec 27 '18 at 9:47
Anonymous1967
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
asked Dec 27 '18 at 9:39
Anonymous1967Anonymous1967
8302826
8302826
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48
add a comment |
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint:
$$sin (a+b)=cos(a)sin(b)+ cos(b)sin(a)$$
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
$endgroup$
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
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
});
}
});
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%2f3053748%2fhow-to-determine-the-dy-term-of-the-differential-of-fx-y-z-sinxy-siny%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
$begingroup$
Hint:
$$sin (a+b)=cos(a)sin(b)+ cos(b)sin(a)$$
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
$endgroup$
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
add a comment |
$begingroup$
Hint:
$$sin (a+b)=cos(a)sin(b)+ cos(b)sin(a)$$
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
$endgroup$
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
add a comment |
$begingroup$
Hint:
$$sin (a+b)=cos(a)sin(b)+ cos(b)sin(a)$$
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
$endgroup$
Hint:
$$sin (a+b)=cos(a)sin(b)+ cos(b)sin(a)$$
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
answered Dec 27 '18 at 9:48
Thomas ShelbyThomas Shelby
3,3571524
3,3571524
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
add a comment |
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
1
1
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
$begingroup$
Oh, oké. I'm so stupid that I didn't even search for that. Thank you for the hint.
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:50
add a comment |
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%2f3053748%2fhow-to-determine-the-dy-term-of-the-differential-of-fx-y-z-sinxy-siny%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
$begingroup$
If the question is $partial f / partial y$ why are you calculating the total differential ?
$endgroup$
– Rebellos
Dec 27 '18 at 9:47
$begingroup$
Because I need it for the total differential. Should I change the question to only the partial derivative?
$endgroup$
– Anonymous1967
Dec 27 '18 at 9:48