1. The problem statement, all variables and given/known data Let [itex]f[/itex] and [itex]g[/itex] be scalar functions of position. Show that: [tex]\nabla f \cdot \nabla(\nabla ^2 g)-\nabla g \cdot \nabla(\nabla ^2f)[/tex] Can be written as the divergence of some vector function given in terms of [itex]f[/itex] and [itex]g[/itex]. 2. Relevant equations All the identities given at https://en.wikipedia.org/wiki/Vector_calculus_identities, I suppose. Especially relevant would be the second derivative and divergence identites. Also, [itex]\nabla ^2 =\nabla \cdot \nabla[/itex] 3. The attempt at a solution After considerable time messing around with various vector identites, I've been able to show the above is equivalent to: [tex]\nabla \cdot (f \nabla (\nabla ^2 g)-g\nabla (\nabla ^2 f))+g(\nabla \cdot \nabla(\nabla ^2 f))-f(\nabla \cdot \nabla(\nabla ^2 g))[/tex] This is painfully close to the result I want, but I can't seem to show that the second and third terms either cancel or are themselves a divergence. I'd really like any hints, and can provide more detail as to the specific identities and manipulations I've used thus far if needed, thanks.