Can the Nabla Operator Be Applied Before Inversion in Tensor Calculations?

[Compengineering]

Dear All,

I'm doing some tensor calculation on the divergence of gradient (of a vector) inverse. Am I allowed to first use the nabla operator on gradient and then inverse the whole product?
In other words, I'm searching for the divergence of a 2nd order tensor which is itself inverse of (gradient of a first order tensor ). Thanks in advance

 

[DuckAmuck]

What do you mean the inverse gradient?

Is it something like \frac{1}{\nabla} \phi?