How can I go about determining the rank of a tensor if I am taking a derivative or an integral?
For example, I have a 2nd order Tensor, $A_{ij}$ and I take the derivative with respect to $x_i$ or $x_j$, how does this affect the rank? $(dA_{ij}/dx_i)$
What about if I were to take an integral in the same fashion? ($\int(A_{ijk} dx_i)$)
I keep seeing something about covariant differentiation of tensors but as this is my first time dealing with tensors, I am not sure how to go about this.
Any help would be greatly appreciated