I believe the jutsu minato left for naruto is ftg and for naruto to complete it meaning using no kunai nor knife why?
minato after fighting tobi realizes something that naruto can't beat tobi without the ftg technic because tobi is fast himself too and will be able to suck naruto in an instant because , he did it against minato and minato knew naruto would have learned rasengan and he knew naruto would be able control the fox too. So he realize that naruto wold need it to fight tobi so he left the basic to jiraiya so that naruto would learnand perfected it but to use it naruto need to fully be able to control his chakra perfectly otherwise he won't be able too.
And since the fox had been at war with naruto, in order for naruto to use it while he was with jiraiya, he ned to control the fox chakra perfectly but couldn't use his because it was there to suppress the fox and that was the problem.
And now that naruto had beaten the fox and control his and the fox chakra after the moment that he got out of the tug war and explained what had happened in the past by his mother and all that, he transform outside his sub conscience and was able to sense kisame due to the fox and naruto own sensory traits and when naruto saw kisame ran to get out of the door to the jinchuuriki door, he realize that he knew of ftg without kunai nor seal so he performed it and it was successful and you could see him jump like his father ftg technic but was not speed but s/p shadowing by kishi himself.
People will say because of the fox but it was wasn't why because mito was a jinchuuri of the ful fox and use the fox chakra better than naruto before the tug war with the fox and mito had the the negative emotion technic but couldn't get the speed why is that.
The fox chakra definitively give more speed but because "that jutsu", naruto was able to perform the ftg technic three times already, one with kisame, the raikage punch and the tail beast bomb again kakashi and guy but all kakashi saw was his sensei flash even with the ms sharigan and guy who is fast couldn't see a thing but said what was that speed because saw the yellow flash and tail beast bomb destroying mountain and kakashi said sensei but was mistaken. But to be honest, naruto still needs more control over it and every time he got more chakra of the fox, he will get better mastery over it.