Find a copy of Chimarvamidium , went into the cave then came up to a door but when I tried to open it , it said the door was barred from inside. The quest put this cave on the map a place I had not been at, but jumped to a place close and found the cave but as I said the door is blocked from inside. Now right away I am saying to myself, this is the wrong enterance but if so why did the map up date to a cave at the wrong end, if it is the wrong one ?

Whenever I find a door that's barred from the inside, there's another way into the area and I end up coming out through the barred door at the end after I've unbarred it from the inside. Look around some more; there should be another way in.

If you are on PC, just disable the door.
The solution is that you are in fact at the wrong entrance and the quest arrows steered you wrong. There is another cave entrance nearby. Use that one.

Most of the dungeons have a "short cut" from the end room right to the beginning. This often involves a drop down or a door only accessible from one side. It makes sense you're seeing the quest marker "behind" this door, as your objective is probably there. But you will have to go the long way round.

Yep, the barred doors are the shortcut out of the end of the dungeon.

Funny thing, I never seem to find the shortcuts when I am at the end of the dungeon......

How can you miss them? Your quest marker leads you right to them.. assuming you're doing a quest while in the cave, of course.

Unless the barred door is obvious, they tend to be behind easy to miss sliding walls that are activated by hard to see pull chains, or a gate that requires a key that is in another section of the dungeon. A key may be in a corpse that a player will overlook because they know the body usually has a small amount of gold and a weapon that is not worth the effort to remove to resell.
Many of us players are older and have eyesight issues.
Using Dawnbreaker has been known to scatter all of the small items inside a dungeon.
Clairvoyance will send a character in a great loop, or retrace the path that a character has already taken.