1) As title says, how does one derive the following equation for covariant derivate of tensor: $A^{\alpha}{}_{;\beta} = A^{\alpha}{}_{,\beta} + \Gamma^{\alpha} {}_{\gamma\beta}A^\gamma$ where $\Gamma^{\alpha}{}_{\beta\gamma} \,$ is a Christoffel symbol of the second kind; and Lie derivative of tensor from http://en.wikipedia.org/wiki/Ricci_calculus#Differentiation ?
And I am having a hard time grapsing what Christoffel of second kind would "symbolize". Can anyone explain this in this derivative context?
Edit: now I understand what and how to derive covariant derivative of tensors, so it's fine to explain lie derivative of tensors only.