This build is for people who have love to jungle and have MAP AWARENESS. pretty basic route.

start at blue, some people say to start at wolves then go blue im not a fan of this mainly because you are saving like 12 seconds and you are not as safe starting there.
go to wolves directly after blue, simple as that use empower with counterstrike wolves are dead in no time i usually use a potion at this point to get me back to around 90% health
go to wraiths same thing as wolves empower and counterstrike and they are done use another potion wile walking to double golems
Kill double golems use another potion and go for red smite should be up at this point and you should be level three so you have leap strike red falls easily
rinse repeat.

map awareness as a jungler SOOOOO important you are not stuck in a lane so u don't have to be AS focused look at mini map ALL THE TIME will save teammates from ganks probably you too.
another reason you have to have map awareness is so that you can GANK accordingly. in my opinion ganking most important part of jungling and when your playing as jax you can gank so easily. keep an eye on you teammates lanes if they are getting their *** handed to them go help even if u dont get a kill the enemy will probably back off letting your teammates get some farm

I gank mid right after i kill red, ALWAYS. get your mid somekind of advantage and he/she should win their lane( should ). So my fav jax combo is leapstrike -> auto attack -> counter strike -> auto attack-> empower as much as u ****ing can till they are dead. i dont tap counter strike a second time. mainly because people will flash as soon as they see you use it most the time my leapstrike is already up and i get my stun off no matter what. THE MORE YOU COORDINATE WITH YOU TEAM THE MORE SUCCESSFUL GANKS YOU WILL HAVE

there are a couple of ways you can build jax. it really depends on what your team needs. if no one on your team was smart enough to be a tank well you can be one if you choose. if your team is low on magic damage u can fill the gap. if your team needs Attack damage well you can cover it. i prefer to go tanky attack damage with some AP thrown in their to kill people who are stacking armor.
For my build
1. cloth armor 5 potions have tested its better than a vamp scepter
2. upgrade to madreds razor but i dont go back untill i can also get boots.
3. uprade razor to wriggles lantern, also upgrade boots to ninja tabi or merc treads depending on enemy team comp
4. Sheen very good if u use skills correctly you can ANNIHILATE pretty much anyone(leapstrike -> auto attack -> counter strike -> auto attack-> empower)
5. Phage: life attack damage and slow very hand when ganking
6. make it all a TRIFORCE. very good for jax
7. at this point you do lots of damage but everyone else isnt as squishy so you can go 2 different directions from here A. get tankier B. get super carry mode and go for penta kills
8. i prefer penta kills so i go for gunblade which makes you hard to kill: thats alot of life leech for jax plus alot of damage for all your skills.
9. Rylais crystal scepter, Health, More damage, EVERYTHING YOU DO SLOWS THEM. sometimes i prefer just to get warmogs depending if im dying too fast if i need to tank more.
10. ATMAS IMPALER this item is a must no matter which way you go you have enough Hp for this item to give you lots of Attack damage. armor. crit