Differentiation of a vektorfield

[klabautermann]

hi!

i flipped through my notes on a class on general relativity this morning and i found an expression which doesn't make sense to me. I am not sure if don't understand the last term in the last equality or it just dosn't make sense. i would appreciate your oppinion.
a,b are abstract indicies. everything else are coordinate indicies.

 

[bloby]

You should explain your notations...

 

[klabautermann]

of course. as i said, a and b are abstract indicies, i,j,m,k are components with respect to a basis. bared and not bared components and differential operators correspond to different coordinate systems.

 

[bloby]

Ok but what are $\partial_a$, the quotation? x is a vector?

 

[bloby]

$\partial_{a}$