I remember once I asked one of my students “今天你得去学校吗？(Do you have to go to school today?) He replied in Chinese: 今天没有课，我不得去学校 (Today we don’t have class, I don’t have to go to school). This sounds really strange in Chinese, because the word 得 (děi: have to, must) is never used in the negative form 不得.
This is a case that demonstrates that in Chinese you can’t always use 不 before a word to negate it. You have to make certain changes or even make clear of the specific meaning of the context before adding 不.
Take 得 as an example. Its negative form is 不用(bú yòng: don’t have to). There are several other words that don’t just use 不 to indicate the negative. Here are a few examples.
可以 (kěyǐ) vs 不可以 (bù kě yǐ)
可以 is an optative verb, means “may”. For example ,我可以进来吗？(May I come in?). The negative form of 可以 is generally “不能(bù néng)” and not “不可以”. For example, if the answer to the question “我可以进来吗” is negative, you should say “对不起，你不能进来". “不可以”is only used to express prohibition. For example,”不可以吸烟” (No Smoking).
要 (yào) vs 不要 (bú yào)
When 要 works as an optative verb, it means “must, to want to do something”. For example, 他要学游泳 (He wants to study swimming). Normally the negative form is “不想”(Xiǎng) or “不愿意” (Bù yuànyì) instead of “不要”. Using the sentence above as an example, you could say ”他不想学习游泳”(He doesn’t want to study swimming)
”不要”is used to express prohibition or persuade others not to do something. For example, 不要浪费水(Don’t waste water).
必须 (bì xǖ) vs 不是必须 (bú shì bì xǖ)
“必须” means “have to”, for example 你必须自己去 (You have to go by yourself). If you’d like to say ”You don’t have to go by yourself”, you’d say “不必”or “无须”. Therefore, the negative form of this sentence should be 你不必自己去or 你无须自己去.
不是必须 means “not required to do it” or “optional”. For example，你不是必须要买这本书 (You don’t really have to buy this book).
很好 (hěn hǎo) vs 不太好 (bù tài hǎo)
Another common example is很好. To negate 很好 you wouldn’t say 不很好. For example ”你最近好不好?” (How have you been recently?). To answer this question in the negative you'd say “不太好” instead of ”不很好”.