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At first, e*ать is much ruder that f*ck.
At second, трахать is really rude here.
Where are you from? Cuz I`m from Russia... And, believe me, I know what is considered to be rude here

Let me explain you.
е*ать is the ruddest one, it`s a foul language. you shouldn`t use this word anywhere.
трахать is rude too, but less. but anyway, you can`t say, for example, your girlfried...