Matrix/Tensor derivative for Stress Tensor

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I need to do define/calculate the following stress tensor in an elegant way:

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

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

$\partial_i v_j := \frac{\partial v_j}{\partial i}$

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!