Are you allowed to use vector analysis identities? What comes to mind is ## \vec{\nabla} \cdot (\phi \vec{A})=\phi \vec{\nabla} \cdot \vec{A}+\vec{A} \cdot \vec{\nabla}\phi##. You can use this to find the term in parentheses and then take its gradient. You should also be allowed to use the expression for the gradient of 1/r.