Others in this thread have pointed out how to channel that frustration and how to avoid letting yourself flame, which is great, there are some awesome tips here. Though as someone who is not that decent of a player most of the time and just got into ranked, let me point out what the other end of it can be like. Whoever has messed up knows they've messed up, they know it's a ranked match and it's something important to the entire team. And even just having that occur will put them in a worse state of mind. They feel bad for messing something up and want to do well, the doubt and extra drive is just going to push them to make more mistakes while trying harder to do the exact opposite.
In the higher stakes scenarios of this game, mentality matters a lot. And when a team member begins to flame, it's going to drive the other player into an even worse mentality and into further mistakes than they've already set themselves up for. And I'm not talking about the flamed champ getting angry or frustrated that they're being flamed, I mean they feel even worse than just from making the initial mistake.
Even less toxic remarks that point it out like: {"?", "wtf", "don't feed", "srsly?"} are driving them lower, harsher things are even worse and it all gets worse when you make the second mistake like dying again early or failing to keep up with your enemy laner.
I know that putting this into words seems like I'm making flamed players sounds overly sensitive to comments, and I actually am in a way, but this really is how it goes down from my rather poor experience in my first placement matches and early bronze.
So flaming or negative commentary does the exact opposite of making things better. Though not doing it will leave you even more frustrated than not putting it out into chat, worsening your own mentality and performance.
Aside from the tips to channel that frustration elsewhere or allowing yourself to cool off a little, I think the best thing you can do is to help them instead of flaming them.
Your top laner dies early because they didn't expect things to go that wrong, they look like an idiot for dying like that. Rather than comment on their idiocy for doing that, tell them it's okay, ask how they were taken down or if they're okay in their lane. If they actually respond with their problem, help them with it.
"Jax burst me early, and I didn't expect it, and I can't farm with him there"
Respond with something like: "that's okay, he's tough to deal with, let him push up to tower and farm or poke him then, you can handle him!"
Something as light as that can make a world of difference to someone who's having trouble and that improvement in mentality will keep them confident and careful. If they're having further problems and you're in a position to head over and help, go for it. Give them a gank when their laner over pushes turret, or guard them while they clear out a wave. This isn't always possible, but when you are in a position to do it, it can mean the difference between a win and loss, you could get a kill in that gank, helping your teammate farm will put them in a better position, keep on giving them tips and helping them out in a friendly way.
Personally, as someone who is the 'helper' ahead of that teammate as he is the idiot top who keeps on dying, helping someone like this relieves my stress about their performance and being helped with any kind of friendliness means a lot and helps performance more than you will ever believe.
It's not something that will relieve everyone's stress though, in the case that you can't help or know that helping isn't going to put you in a better frame of mind, refer to the other tips in this thread and maybe throw down an "it's alright :)" in chat when that top laner messes up, it will still help out their mentality going back in if they know their teammates don't hate them for goofing up.
I hope this rant/thing is of some use
