I have an slx rear derailleur and deore shifters, I’ve been having shifting problems and I’ve got the bike upside down and adjusted the derailleur as per instructions on the internet, the shifting is much smother now and I can get into the top and bottom gears the the second smallest sprocket is always missed when shifting down, but not when moving up into easier gears.

If this normal and can I fix it?

Give cable adjuster half a turn anti clockwise to put a little more tension in it, sounds like you are 95% there.

I just gave it another tweak, adding more tension doesn’t work

I’m 99% sure that the chain and little ring has worn out, they’ve done something like 5,500 miles since new. Is there a way I can check without buying a new chain/cassette/middle ring ? I don’t have a chain measuring tool.

Definitely worth checking your mech hanger alignment. It can look straight but be bent enough to cause this kind of malshifting

looking at it it could be a few mill out of wack, but the 11 tooth sprocket is definitely shark tooth like and I should replace the outer ring as it’s too small, which is my the 11 is so worn. My main problem is the chain skipping so if the problem is still there i’ll look for a new hanger and maybe a new derailleur.

Skipping is usually due to 2 things IME.
1. bent hanger
2. Cable stick

for 1 replace the hanger. If that’s not the problem it’s always good to have a spare
for 2 replace the cables and use a full outer length.

if neither of those work, it is probably due to the derailleur being bent. That’s unusual and unlucky.

My first thought from your OP was a bent hanger, but my second would be suspicion of a chain that should have been replaced a while back. Your following post makes me veer in that direction and as you’ve figured out, it isn’t going to just be a new chain..

If you have really have ridden over 5500 miles on the drive you need to replace the lot.

It’s hard to tell exactly, I’ve commuted for two and a half years. first year and a half was 10 miles each way on a flat non tracked cycle track and i reckon I probably missed about 6 months overall. Second job was 8 miles each way but with hills and only on the road so I got a fixed bike (well I’m on my second now) but when it didn’t work I used the original bike. So it could be as little as 4,000 miles.

I hope I won’t have to replace the cables or the derailleurs.