Hi! I'm Derps. Welcome to my Jax guide for low elo.
Wooph! My first guide. I'll do my best to keep this updated however life may interrupt. I'm a jungle main and in my opinion while Jax may not be the most interesting champ in terms of skills, his combos are easy to do and rewarding to pull off. Jax is a champion that in low elos can carry really hard if the enemy team doesn't know how to counter him and as such is good for getting out of elo hell.
Welp. Here goes...

Jax is an extremely fun champion with little difficulty to play. He is very good in elo hell as often people don't know how to counter a Jax jungle, which you can take advantage of.
-Pros
-Good clear
-Strong mid game
-Super fast attack speed
-Good in 1v1s
-Cons
-Not very mobile
-AA reliant
-Little CC

As he's a jungler with fairly limited mobility, I take both Smite and Flash as they are pretty standard for most junglers and very useful. Smite is essential on almost all junglers, and Jax is no exception. Flash is essentially a free escape or engage and if used wisely can win teamfights and steal objectives.

I took 18 12 0 because that's pretty standard for Jax. Most of these masteries are pretty normal for Jax anyway.
Fury is the obvious choice given that Jax is very AA oriented and free attack speed is always nice.
Fresh Blood is next because its essentially free damage every time you go in for a teamfight.
Natural Talent because free ad and ap as long as you last until 18
Double Edged Sword was an obvious pick because while Jax isn't a tank, he can take bit of damage, and the extra damage dealing is very useful in 1v1s.
Battering Blows because Jax is once again ad oriented and as such the armor pen is always nice
Finally, Fervor of Battle because it synergises well with Jax the Machine Gun, no surprise there.
For Cunning,
Savagery is an obvious choice for Jax as he is a jungler, and as such auto attacks a lot of monsters.
Assassin is my personal choice as it gives me an edge in 1v1s, which are what Jax is made for. However, as he's going jungle, you could just as easily take Runic Affinity . It just comes down to personal preference.
Merciless is nice because once again, it gives him an edge in 1v1s. Whittle the enemy down to 40%, then bring the pain.
Finally, Greenfather's Gift is really good at shredding tanks once you start a gank and combined with some careful timing can give your ambushes a lot more punch.

Really nothing to see here. This is just my personal preference and it might be weird but I enjoy playing machine gun Jax, so quints of attack speed, some attack damage, more attack speed and some scaling magic resist and health.

I always take e first, followed by w, then q, then max w. Counter Strike is very good as a first ability in jungle as it allows you to tank a few hits from a buff before losing any health. Empower is next because it is an underappreciated damage boost that can do some substantial damage. Leap Strike good to have a point of for ganks but other than that not very good for clearing so I don't max it until I have to.

Jax has one combo he relies on quite a bit, and that is Counter Strike, Leap Strike, Empower, as this allows him to jump in, take a few autos and then stun, then finish them off with some more autos and his w.

Wowsers! You've made it this far without exiting in disgust! Jax is a super fun champ with a ton of damage output and serious 1v1 potential. I hope this guide helped a bit if you wanted to read up on Jax. Thanks very much for reading, and feel free to leave any questions / queries / hate speech in the discussion. I'll make sure to read them all.
Cheers!