Main Question or Discussion Point
I am trying to understand the notion of a covariant derivative and Christoffel symbols. The proof I am looking at starts out with defining a tensor, Tmn = ∂Vm/∂xn where V is a covariant vector. I am having a mental block with regard to the indeces. How is it that the derivative of a covariant vector (1st order tensor) be consider to be a 2nd order tensor?