There are several occasions when Inuyasha tries to kill Kagome, though he is usually either being possessed or has turned full demon. Inuyasha would NEVER in his right mind attempt to kill Kagome. 1) So in the 2nd episode Inuyasha does try to kill Kagome to get the jewel. However, he doesn't seem to actually be trying to take her life, only scare her. But he does take a few swipes at her with his claws. 2) There are several times when Inuyasha turns full demon and just tries to kill everyone in the surrounding area, including Kagome. Though he still seems to have some control and can distance himself from here. Examples of this can be seen in episode 52, episode 21 and 22 of TFA, and the 3rd movie just to name a few. Episode 21 is the closest Inuyasha has ever come to killing Kagome himself as he is full demon and injures her with his claws, however he is able to push her away from him so he can't hurt her anymore, though he has no recollection of this and fears that he has killed Kagome as he has her blood on his hands.