Here are the homework problems for reference. I will type additional details under them. I'm having a lot of trouble and I'm completely lost.

Diff Geometry problem | Flickr - Photo Sharing!

formula 2(b) mentioned in the link/problem above:

Covariant derivative formula | Flickr - Photo Sharing!

Second problem:

Diff Geom problem 2 | Flickr - Photo Sharing!

My main issue with the first problem is that I get a huge mess that can't possibly be correct whenever I plug in the equations for X and Y, and try to differentiate between i, j, k, etc.

My main issue with the second is that I don't understand how to calculate the covariant derivative (trianglea'(t) of a'(t), as mentioned in 4(a)), nor how to prove that it is geodesic.

Thanks in advance for your help.