How does this bundle of gradients and a divergence equal these gradients and Hessians?

Question

In words it may be vague, but my question is: why does $$ \nabla \cdot (\nabla f \cdot \nabla g) = Hess(f) \cdot \nabla g + Hess(g) \cdot \nabla f) $$ In d dimensions?

Edit: After the hint, I was able to manage the problem. Thanks to Blue Raincoat.