The sentence "You should of known better" derives from "You should've known better"; "should of" sounds about like the way you say "should've".

Of course "should've" is a contraction of "should have" - consequently it is correct to say either "You should have known better" or (being a bit informal) "You should've known better" but it is incorrect to WRITE "You should of known better" instead of "You should've known better."

No

The sentence "You should of known better." derives from "You should've known better."; "should of" sounds about like "should've". Of course "should've" is a contraction for "should have" so the correct sentence is either "You should have known better." or (if speaking informally and using contractions) "You should've known better." Writing the sentence as "You should of known better." instead of "You should'veknown better." is INCORRECT.