Partial derivative with respect to three variables
Clash Royale CLAN TAG#URR8PPP
5
I just started learning LaTeX and I am facing problem in writing the following equation, can anyone please help me out?
symbols
edited Feb 22 at 14:03
Bernard
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
add a comment |
5
I just started learning LaTeX and I am facing problem in writing the following equation, can anyone please help me out?
symbols
edited Feb 22 at 14:03
Bernard
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
add a comment |
5
5
5
I just started learning LaTeX and I am facing problem in writing the following equation, can anyone please help me out?
symbols
edited Feb 22 at 14:03
Bernard
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
I just started learning LaTeX and I am facing problem in writing the following equation, can anyone please help me out?
symbols
symbols
edited Feb 22 at 14:03
Bernard
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
edited Feb 22 at 14:03
Bernard
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
edited Feb 22 at 14:03
Bernard
173k776205
edited Feb 22 at 14:03
Bernard
173k776205
edited Feb 22 at 14:03
Bernard
173k776205
173k776205
asked Feb 22 at 13:41
shadow khshadow kh
1284
asked Feb 22 at 13:41
shadow khshadow kh
1284
asked Feb 22 at 13:41
shadow khshadow kh
1284
1284
add a comment |
add a comment |
5 Answers
5
active
oldest
votes
8
A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:
documentclassarticle
usepackagemathtools, diffcoeff
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*diffp[k_1,k_2,l]u_0
x_1, x_2, t leq C
]
enddocument
answered Feb 22 at 14:06
BernardBernard
173k776205
I didn't know aboutdiffcoeff. Nice. Off topic:k_1+k_2+ljust to be compatible with order of powers in denominator? :-)
– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powersk_1,k_2andlshould be applied to the wholepartial <variable>thing.
– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
add a comment |
6
You could write
[leftlvertfracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^lrightrvert
leq C]
edited Feb 22 at 13:52
Sigur
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
add a comment |
5
Like this?
documentclassreport
usepackageamsmath
begindocument
[ Bigglvert
fracpartial^k+lu_0
partial^k_1x_1,
partial^k_2x_2,
partial^lt
Biggrvert leq C,
]
enddocument
answered Feb 22 at 13:46
SigurSigur
26.1k457142
The notation here is wrong I’m afraid. Thek_1,k_2andlshould follow the variables, not thepartialsigns. See i.stack.imgur.com/Jc3v8.png
– Ruixi Zhang
Feb 23 at 13:04
add a comment |
4
one more variation ...
documentclassarticle
usepackagemathtools
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*fracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^l leq C
]
enddocument
answered Feb 22 at 13:49
ZarkoZarko
127k868167
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part oflatexcode, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select optionShow Ink selection ...
– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply useboxed...inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space withhspaceorqquad
– Jhor
Feb 22 at 20:55
add a comment |
1
documentclassarticle
begindocument
$ left | fracpartial^k+1u_0partial x_1^k_1 partial x_2^k_2 partial t^l right | leq C $
enddocument
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
add a comment |
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5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
8
A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:
documentclassarticle
usepackagemathtools, diffcoeff
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*diffp[k_1,k_2,l]u_0
x_1, x_2, t leq C
]
enddocument
answered Feb 22 at 14:06
BernardBernard
173k776205
I didn't know aboutdiffcoeff. Nice. Off topic:k_1+k_2+ljust to be compatible with order of powers in denominator? :-)
– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powersk_1,k_2andlshould be applied to the wholepartial <variable>thing.
– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
add a comment |
8
A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:
documentclassarticle
usepackagemathtools, diffcoeff
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*diffp[k_1,k_2,l]u_0
x_1, x_2, t leq C
]
enddocument
answered Feb 22 at 14:06
BernardBernard
173k776205
I didn't know aboutdiffcoeff. Nice. Off topic:k_1+k_2+ljust to be compatible with order of powers in denominator? :-)
– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powersk_1,k_2andlshould be applied to the wholepartial <variable>thing.
– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
add a comment |
8
8
8
A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:
documentclassarticle
usepackagemathtools, diffcoeff
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*diffp[k_1,k_2,l]u_0
x_1, x_2, t leq C
]
enddocument
answered Feb 22 at 14:06
BernardBernard
173k776205
A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:
documentclassarticle
usepackagemathtools, diffcoeff
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*diffp[k_1,k_2,l]u_0
x_1, x_2, t leq C
]
enddocument
answered Feb 22 at 14:06
BernardBernard
173k776205
answered Feb 22 at 14:06
BernardBernard
173k776205
answered Feb 22 at 14:06
BernardBernard
173k776205
answered Feb 22 at 14:06
BernardBernard
173k776205
173k776205
I didn't know aboutdiffcoeff. Nice. Off topic:k_1+k_2+ljust to be compatible with order of powers in denominator? :-)
– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powersk_1,k_2andlshould be applied to the wholepartial <variable>thing.
– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
add a comment |
I didn't know aboutdiffcoeff. Nice. Off topic:k_1+k_2+ljust to be compatible with order of powers in denominator? :-)
– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powersk_1,k_2andlshould be applied to the wholepartial <variable>thing.
– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
I didn't know about
diffcoeff. Nice. Off topic: k_1+k_2+l just to be compatible with order of powers in denominator? :-)– Sigur
Feb 22 at 14:09
I didn't know about
diffcoeff. Nice. Off topic: k_1+k_2+l just to be compatible with order of powers in denominator? :-)– Sigur
Feb 22 at 14:09
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
@Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator.
– Bernard
Feb 22 at 14:15
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powers
k_1, k_2 and l should be applied to the whole partial <variable> thing.– Ruixi Zhang
Feb 23 at 13:05
Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powers
k_1, k_2 and l should be applied to the whole partial <variable> thing.– Ruixi Zhang
Feb 23 at 13:05
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature?
– Bernard
Feb 23 at 13:54
add a comment |
6
You could write
[leftlvertfracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^lrightrvert
leq C]
edited Feb 22 at 13:52
Sigur
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
add a comment |
6
You could write
[leftlvertfracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^lrightrvert
leq C]
edited Feb 22 at 13:52
Sigur
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
add a comment |
6
6
6
You could write
[leftlvertfracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^lrightrvert
leq C]
edited Feb 22 at 13:52
Sigur
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
You could write
[leftlvertfracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^lrightrvert
leq C]
edited Feb 22 at 13:52
Sigur
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
edited Feb 22 at 13:52
Sigur
26.1k457142
edited Feb 22 at 13:52
Sigur
26.1k457142
edited Feb 22 at 13:52
Sigur
26.1k457142
26.1k457142
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
answered Feb 22 at 13:45
José Carlos SantosJosé Carlos Santos
8571217
8571217
add a comment |
add a comment |
5
Like this?
documentclassreport
usepackageamsmath
begindocument
[ Bigglvert
fracpartial^k+lu_0
partial^k_1x_1,
partial^k_2x_2,
partial^lt
Biggrvert leq C,
]
enddocument
answered Feb 22 at 13:46
SigurSigur
26.1k457142
The notation here is wrong I’m afraid. Thek_1,k_2andlshould follow the variables, not thepartialsigns. See i.stack.imgur.com/Jc3v8.png
– Ruixi Zhang
Feb 23 at 13:04
add a comment |
5
Like this?
documentclassreport
usepackageamsmath
begindocument
[ Bigglvert
fracpartial^k+lu_0
partial^k_1x_1,
partial^k_2x_2,
partial^lt
Biggrvert leq C,
]
enddocument
answered Feb 22 at 13:46
SigurSigur
26.1k457142
The notation here is wrong I’m afraid. Thek_1,k_2andlshould follow the variables, not thepartialsigns. See i.stack.imgur.com/Jc3v8.png
– Ruixi Zhang
Feb 23 at 13:04
add a comment |
5
5
5
Like this?
documentclassreport
usepackageamsmath
begindocument
[ Bigglvert
fracpartial^k+lu_0
partial^k_1x_1,
partial^k_2x_2,
partial^lt
Biggrvert leq C,
]
enddocument
answered Feb 22 at 13:46
SigurSigur
26.1k457142
Like this?
documentclassreport
usepackageamsmath
begindocument
[ Bigglvert
fracpartial^k+lu_0
partial^k_1x_1,
partial^k_2x_2,
partial^lt
Biggrvert leq C,
]
enddocument
answered Feb 22 at 13:46
SigurSigur
26.1k457142
edited Feb 22 at 13:53
answered Feb 22 at 13:46
SigurSigur
26.1k457142
answered Feb 22 at 13:46
SigurSigur
26.1k457142
answered Feb 22 at 13:46
SigurSigur
26.1k457142
26.1k457142
The notation here is wrong I’m afraid. Thek_1,k_2andlshould follow the variables, not thepartialsigns. See i.stack.imgur.com/Jc3v8.png
– Ruixi Zhang
Feb 23 at 13:04
add a comment |
The notation here is wrong I’m afraid. Thek_1,k_2andlshould follow the variables, not thepartialsigns. See i.stack.imgur.com/Jc3v8.png
– Ruixi Zhang
Feb 23 at 13:04
The notation here is wrong I’m afraid. The
k_1, k_2 and l should follow the variables, not the partial signs. See i.stack.imgur.com/Jc3v8.png– Ruixi Zhang
Feb 23 at 13:04
The notation here is wrong I’m afraid. The
k_1, k_2 and l should follow the variables, not the partial signs. See i.stack.imgur.com/Jc3v8.png– Ruixi Zhang
Feb 23 at 13:04
add a comment |
4
one more variation ...
documentclassarticle
usepackagemathtools
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*fracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^l leq C
]
enddocument
answered Feb 22 at 13:49
ZarkoZarko
127k868167
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part oflatexcode, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select optionShow Ink selection ...
– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply useboxed...inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space withhspaceorqquad
– Jhor
Feb 22 at 20:55
add a comment |
4
one more variation ...
documentclassarticle
usepackagemathtools
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*fracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^l leq C
]
enddocument
answered Feb 22 at 13:49
ZarkoZarko
127k868167
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part oflatexcode, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select optionShow Ink selection ...
– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply useboxed...inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space withhspaceorqquad
– Jhor
Feb 22 at 20:55
add a comment |
4
4
4
one more variation ...
documentclassarticle
usepackagemathtools
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*fracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^l leq C
]
enddocument
answered Feb 22 at 13:49
ZarkoZarko
127k868167
one more variation ...
documentclassarticle
usepackagemathtools
DeclarePairedDelimiterabslvertrvert
begindocument
[
abs*fracpartial^k+lu_0
partial x_1^k_1partial x_2^k_2partial t^l leq C
]
enddocument
answered Feb 22 at 13:49
ZarkoZarko
127k868167
answered Feb 22 at 13:49
ZarkoZarko
127k868167
answered Feb 22 at 13:49
ZarkoZarko
127k868167
answered Feb 22 at 13:49
ZarkoZarko
127k868167
127k868167
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part oflatexcode, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select optionShow Ink selection ...
– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply useboxed...inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space withhspaceorqquad
– Jhor
Feb 22 at 20:55
add a comment |
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part oflatexcode, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select optionShow Ink selection ...
– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply useboxed...inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space withhspaceorqquad
– Jhor
Feb 22 at 20:55
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
How did you produce the frame around the image?
– Sigur
Feb 22 at 13:55
@Sigur, it is not part of
latex code, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select option Show Ink selection ...– Zarko
Feb 22 at 14:01
@Sigur, it is not part of
latex code, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select option Show Ink selection ...– Zarko
Feb 22 at 14:01
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Ah, OK. I use Shutter. Maybe there is such frame option there.
– Sigur
Feb 22 at 14:02
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created.
– Sigur
Feb 22 at 15:03
For the frame around formula in LaTeX, simply use
boxed... inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space with hspace or qquad– Jhor
Feb 22 at 20:55
For the frame around formula in LaTeX, simply use
boxed... inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space with hspace or qquad– Jhor
Feb 22 at 20:55
add a comment |
1
documentclassarticle
begindocument
$ left | fracpartial^k+1u_0partial x_1^k_1 partial x_2^k_2 partial t^l right | leq C $
enddocument
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
add a comment |
1
documentclassarticle
begindocument
$ left | fracpartial^k+1u_0partial x_1^k_1 partial x_2^k_2 partial t^l right | leq C $
enddocument
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
add a comment |
1
1
1
documentclassarticle
begindocument
$ left | fracpartial^k+1u_0partial x_1^k_1 partial x_2^k_2 partial t^l right | leq C $
enddocument
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
documentclassarticle
begindocument
$ left | fracpartial^k+1u_0partial x_1^k_1 partial x_2^k_2 partial t^l right | leq C $
enddocument
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
edited Feb 22 at 13:48
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
answered Feb 22 at 13:46
Sina AhmadiSina Ahmadi
77338
77338
add a comment |
add a comment |
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