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「食{た}べる」 can be negated as 「食べない」. 「美{うつく}しい」 can be negated as 「美しくない」. etc. etc.
Can you negate 「べき」as in:
「明日は受験なので、勉強するべきです。」(Since you are taking a test tomorrow, you should study.)
「明日は受験なので、遊ぶべき___。」(Since you are taking a test tomorrow, you should not play around.)
Every part of speech in Japanese seems negatable, but I can't figure-out how to negate 「べき」。「遊ばないべきです」 is not the answer I am looking for.
べき is a fun part of modern Japanese grammar with odd rules probably best explained using the historical explanation.
べし used to be a 助動詞{じょどうし} (auxiliary).
Connecting to things before it: べし followed the 終止形{しゅうしけい} (conclusive form) normally, and with ラ変{へん} verbs it followed the 連体形{れんたいけい} (adnominal form). (NB: One could think of it as u being part of the morpheme: -ube-.)
Connecting to things after it: べし inflected like an adjective:
未然形 ｏ べから
連用形 べく べかり
終止形 べし ｏ
連体形 べき べかる
已然形 べけれ ｏ
命令形 ｏ ｏ
Evolution: べし did not evolve like a normal adjective would (i.e., become べい and end be able to sentences), but instead did something weird, presumably due to its status as a 助動詞 and not a 形容詞.
Currently, べき behaves like this:
Connecting to things before it: べき still behaves completely like a 助動詞 in this sense -- you need a fully surfaced verb to connect it to:
ｘ猫だべき
ｘ猫なべき
ｘ猫のべき
ｘ猫べき
ｏ猫であるべきｘ熱いべき
ｏ熱くあるべき
Connecting to things after it: This is the odd bit. べき behaves a lot like 同じ when connecting to things after it: For nominals, べき it connects directly. When concluding sentences, it takes the copula (which can be ∅ in informal speech, but I think most people think of the copula still being there).
やるべきこと
行くべきだ
(Side note: there is also べし still around for ending sentences which people use when trying to sound archaic or pompous or whatever, but amusingly, some people say べしだ which means some people treat it as a noun also.)
As written in other answers, but now with reasons:
However, there is a lingering thing that needs to be discussed:
You should not [eat the cake]. ⇒ You shouldn't eat the cake.
You should [not eat the cake].
In English (at least in my opinion), there is a subtle ambiguity in focus between "You should not eat the cake." One way to read it is that there is an action, and you should not take it. The other way is that there is an action of not doing something, which you should take. The former way can be contracted but the latter cannot.
(If you can't tell the difference, consider the dialogue: "Should I eat the cake, or should I not eat the cake?" "You should not eat the cake.")
This is of course very subtle. What's the situation in Japanese?
In Japanese, you use べきでない for both. Since the negation is all the way on the outside, it sort of suggests the "You should not [eat the cake]." nuance, and if there is a situation that really needs the "You should [not eat the cake]." nuance, you don't have anything like ないべき to use. In the case where I really care about such a nuance, I think I would use ない方がいい.
Most naturally, you can use one of the two below.
「[遊]{あそ}ぶべきでない。」
「遊ぶべきではない。」
The second one places more emphasis on the negation.
There is a word that is not used so frequently in everyday speech but that nonetheless performs this task: べからず. You use it in the same was as べき/べし. An example on alc shows the following sentence:
自然を侮るべからず。
Don't underestimate nature.
I am not a native of course, so I can't comment on precisely where you should and shouldn't use it, but I'd say in most situations, unless you know it's OK to use it, you should just opt for the simpler ～べきではない or ～しないこと or ～してはいけない or something similar (aka see 非回答者's post). In general searching I see it also used in the phrase 「べからず集」 to refer collectively to things you should not do (like as a list).
