derivative of the laplacian operator

Question

Assumes $\Delta \phi = \nabla\cdot\nabla\phi$ and $$ f(\phi) = \Delta\phi $$ then, what is $$ \frac{df(\phi)}{d\phi} $$

no clue how to solve this

Answer 1

In a rough sense, if you are taking a functional derivative, you can see $\Delta \phi$ as an infinite dimensional matrix multiplied to the vector space of functions, so the result is a constant matrix $\Delta$.