Depending on which platform you're using, Duolingo does have a tips page accessed from the lightbulb icon when starting a lesson: https://www.duolingo.com/skill/de/Verbs-Imperative/tips-and-notes
If you are on a platform without the Tips & Notes, you can find them on the unofficial Duolingo companion site DuoMe: https://www.duome.eu/tips/en/de
Getting this far into the course, it is also worthwhile searching the internet for other resources. There are many out there, such as this: https://deutsch.lingolia.com/en/grammar/verbs/imperative
This is a strange situation in Duolingo. It offered me a blank followed by "nicht traurig." Well, either "Sei" (singular) or "Seid" (plural) could fit. But there was no audio, so there was no way to tell which was wanted. I guessed "Sei," but Duolingo said I was wrong. It wanted plural. I reported that "something else" is wrong with this question, but knew no way to give an explanation except by commenting like this. Thank you!
The rule for simple sentences is that 'nicht' comes after: subject, verb, all objects; and before: everything else (expressions of time, place, and manner, predicate adjectives, separable prefixes, infinitives, past participles). Exceptions: though 'nicht' comes before general time expressions (Ich gehe nicht oft.) it comes after specific time expressions (Ich gehe heute nicht.). You may also wish to place special stress when negating something, and 'nicht' can come before that object, for example: Ich gehe nicht heute (sondern morgen).
It's interesting, but probably amounts to a dialect variation, which doesn't lined up with the textbook standard of language (which happens everywhere in every language). I'm very surprised @ThomasGhob that you learned it that way, because the correct (standard German) form is just 'seid' as @biertopf wrote.
Infinitives always go at the end.
This kind of command using an infinitive is thus not a complete sentence, I suppose, since there is no finite verb.
You can often find it on signs that don't address a specific person but the public in general (anyone who reads it), e..g Bitte nicht aus dem Fenster lehnen (Please do not lean out of the window) or Raum nach Gebrauch wieder abschließen (Lock the room after using it).
"Sei" is also a correct answer. "Sei" is the singular (informal) form, for if you're talking to one person, and "seid" is the plural (informal) form, for multiple people.
For most verbs, the plural imperative form will end with "-t" ("Spielt nicht im Haus"), but "sein" is irregular and doesn't do this.
Please read all of the comments on this page. The possible forms for the imperative in this sentence have been mentioned several times.
Also, arbeiten does not labour here... I mean does not work. Würde ... auch gehen? or Wäre ... auch richtig/möglich? would be better alternatives.
So "be not sad" can be considered grammatically correct; however, because it is not modern English, it is not accepted. In the same way that English no longer uses "thou/thee/thine", or the "-eth" ending (like one might find in the Bible or Shakespeare's works), the construction is archaic or poetic.
Why 'sei nicht traurig' is incorrect?
If you came to this sentence discussion, you probably had either a listening exercise ("type what you hear") or a translation exercise from German to English.
If it was a listening exercise: your answer is incorrect because the voice says seid, not sei.
If it was a translation exercise: your answer is incorrect because sei nicht traurig is not an English sentence.
For a more precise answer, please show us exactly what kind of exercise you had and exactly what you typed -- upload your screenshot to a website somewhere (e.g. imgur) and tell us the URL of the image.
seems to me be not sad is a reasonable slightly poetic way of saying the same thing
and should be accepted
Please use standard written English -- the kind of language you would use for a school assignment.
Don't use colloquial language. Don't use poetic language. Don't use archaic language.
Just use standard written English, please.
An exclamation point is not needed in either the German or the English. It's just used to add emphasis, so it's never necessary grammatically. You can add an exclamation point to any sentence to show shouting, excitement, anger, etc.
So an exclamation point would probably indicate that I was shouting "Don't be sad" or saying it urgently or excitedly, which is unlikely given the sentence. The period makes more sense here.
Even though my answer means the same and displays an understanding?
Yes. Because Duo doesn't understand English or German, so it has no way to know what answers indicate an understanding. It can only compare the response to a list of acceptable answers that volunteers have compiled.
And we're not going to add dozens of literary, "technically correct", or otherwise non-standard versions.
The problem is that, even though you know you understand it, the app cannot necessarily know that with such a literal translation which is not not used in common spoken English (neither US nor UK English). Using outdated or old-fashioned literary phrases does not display understanding of modern language. If people said "be not sad" to me, I would assume that they were learning the language, not that they were fluent English speakers.