I have some expression of the form
$$(\nabla_i \nabla^2 f)_{hj}$$
I want to rewrite it, such that I get s.t. like
$$ (\nabla_i \nabla_h \nabla f )_j +??$$
I know that
$$\nabla^2_{ij} f= \nabla_i\nabla_j f - \nabla_{\nabla_i \partial_j} f$$
but I don't know how to use this for my expression.