### Matrix/Tensor derivative for Stress Tensor

I need to do define/calculate the following stress tensor in an elegant ~~way (given in latex-syntax):~~way:

~~T_{i,j} ~~$T_{i,j} := -p \delta_{i,j} + \eta (\partial_i v_j + \partial_j ~~v_i)~~v_i)$

where i,j can be x,y,z and

~~\partial_x v_y ~~$\partial_i v_j := \frac{\partial ~~v_y}{\partial x}~~v_j}{\partial i}$

I've found the sage-function kronecker_delta for the first term, but I am having problems with the two partial derivatives.

Thanks in advance!