Since no one else has posted anything, I figure I'll give it a try.

Note: I'm not the strongest at matrix calculus so take this with a grain of salt.

You're taking the derivative of a scalar function with respect to a matrix (3 x 3). So our result is going to be a (3 x 3) matrix as well.

It looks like the difficulty here is finding .

So we know that this derivative is a 3 by 3 matrix .

And you say you have the derivative of

So I think the rest should be doable?

This may help also

Matrix Calculus