# The result if order of two filter are reversed

1. Apply the Composite Laplacian Filter first, then apply the gaussian filter.
2. Apply the gaussian filter first, then apply the composite laplacian filter.

My work as below: Here we assume the original image is function $$f(x,y)$$ $$(1): (f-\nabla^2f)\ast G = f \ast G - \nabla^2f \ast G$$ $$(2): (f \ast G) - \nabla^2(f \ast G) = f \ast G - f \ast \nabla^2G$$

I am wondering the statement $$\nabla^2f \ast G = f \ast \nabla^2G$$ is true or not.