You can do general matrices too, what do you have in mind? aa[x_] = {{1, 2}, {3, 4}} x bb[x_] = {x^2, x^3} D[ a[x].b[x] , x, x] (* for any suitable tensors *

You can do general matrices too, what do you have in mind? aa[x_] = {{1, 2}, {3, 4}} x bb[x_] = {x^2, x^3} D[ a[x].b[x] , x, x] (* for any suitable tensors *) % /. {a -> aa, b -> bb}