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嫉妒，忌妒，妒嫉，妒忌？

Hello happyrabbit,

There are slight differences in the meaning of those terms as follows:

嫉妒 (jidu)to be jealous , to envy
忌妒 (jidu )to be jealous of ,envy
妒 (du) to envy 嫉 (ji) jealousy , be jealous of
妒忌 ( duji) jealous , jealousy

嫉妒，be jealous of, envy
妒忌，忌妒，they are the same meaning, envy those who are more capable and talented, to harbour a grudge against them.
there is no 妒嫉，people make it up

pay attention to the pronounciation
嫉ji2 妒du4
忌ji4 妒du4

妒嫉 DOES exist in the chinese classics.

an example paragraph cited from 漢書
班固 漢書 卷三十六 楚元王傳第六 ""猶欲保殘守缺，挾恐見破之私意，
而無從善服義之公心，

或懷妒嫉，

不考情實，雷同相從，隨聲是非，抑此三學，以《尚書》為備，
謂左氏為不傳《春秋》，豈不哀哉！""

the following explanation is cited from
http://www.epochtimes.com/b5/9/9/3/n2644615.htm

賞析：《毛詩．序》曰：「〈螽斯〉，后妃子孫眾多也。
言若螽斯不妒忌，則子孫眾多也。」
上一篇的《毛詩．序》用了「嫉妒」這個詞，這一篇用「妒忌」。
其實，這個詞最早的用法是「妒嫉」，三個詞的意思都一樣。
這是兩個同義字組成的詞組，古人寫文章詩賦，
有時出於押韻等目的，就有可能更換次序使用，
猶如「宇宙」和「宙宇」之意思相同。

Hello, happyrabbit.

Wow, even I am a Chinese, I really got dizzy. 嫉妒 is more common. 忌妒 is also right.

妒嫉，妒忌.... I have no idea.

Sorry for giving the wrong information, but I have looked 现代汉语词典(商务印刷馆）before answer this question，there isn't 妒嫉。