Kakashi was taught the rasengan. He tried adding in his element (lightening) to combine with it but ultimately failed (and thus i think the raikiri/chidori was formed lol)
You can't copy the rasengan anyway, as it's just chakra manipulation, if you could copy that sasuke would have been able to copy the tree climbing technique or the chidori instantly, and i'm sure he would have copied the rasengan if he could.
he could never copy rasegan, cause rasegan is different from other techs 'cause you dont form seals... if rasengan used seals dan kakashi:kakashi: could copied the tech
kakashi's raikiri was created by kakashi 'cause he accidentely joined a electric style to his rasengan, formed then raikiri
well its kind of obvious that Kakashi would have learned it from his former sensei being as Kakashi was the 4ths favourite student and the ability that Kakashi possesses.