I agree, but I don't actually know how to skill it. So I will definallity change it. And about the Deathcap, It is a great item for Jax, since it Adds alot of Damage to your skills W and Q, But also gives you alot of HP.

I dislike this build. Even though the Rabbadon deathcap and Lich bane combo is really good, it still really bad seeing you maxed Leap Strike 2nd, and at lvl 15. By lvl 9 you SHOULD max it, I don't know why everyone adds empower, when it only gives a damage boost, but Leap Strike reduces the cooldown too. The % is higher, meaning its better late game yes, but its cooldown is STILL too long to be effective in my opinion. With it maxed at lvl 9, you can easily rush into a team fight and rush out afterwards for safety, if your team is regrouping/lost. There is not much point in putting in Hextech Gunblade and Guinsoo if your attack speed will still be ****, lich bane and rabbadon's combo doesn't rely on attack speed anyway, so you might as well get CDR for you, seeing you are a higher based on magic damage anyway, meaning Will of the Ancients suit you better (Your AD damage is weak AND slow, only higher than spellcasters and tankers, never as good as carries) Hextech Gunblade is left for HYBRIDS and not AP. For my AP Jaxes, I never get Gunblade seeing you don't empower leapstrike unless you want to regen HP, besides which, I only empower hit, leapstrike hit, counterstrike, hit and continue that combo for lich bane. So either go for some other items replacing Rylai (its useless seeing you only slow 1 target OR many targets after a stun) or Hextech and Guinsoo (Only good early game to mid game combo, not good elsewhere). I suggest some items like Malady which provides attack speed and reduced Mr to target, which is good if you go hybrid attack speed and AP Jax.

Not the ultimate OP build .. i beat it :)
But definitely not bad

I liked the item build a lot up until Rabadon's Deathcap. It's really not necessary for Jax as he's a hybrid. Unless you're completely rolling the other team you won't need that much ability power. If you still wanna go with the ability power of Needlessly Large Rod I would suggest Zhonya's Hourglass instead as it gives you the armor and the helpful active. Other then that this guide looks good.