T1. Covarient Derivative:

a) Co-variant Derivative of First Rank Tensor: .

>> Solution:

We know that:
                                                                                              -------------------- (1)
Differentiating with respect to . We get,


                                                               -------------------- (2)

Now,
                                     -------------------- (3)

Put this value of equation (3) in equation (2). We get,











In the last term: . Then we get,





                    -------------------- (4)

The term:     is a co-variant tensor of first rank, called the Co-variant derivative of with respect to .

It is denoted as:

    called the Co-variant derivative.