If you have I=∫∫dxdy [∇(adsbygoogle = window.adsbygoogle || []).push({}); _{x}∇_{y}δ(x-y)] f(x)g(y)

where ∇_{x}is the derivative with respect to x (and similarly for y), then doesn't it matter which order you take the derivatives? For example:

I=∫∫dxdy f(x) ∇_{x}[∇_{y}δ(x-y)] g(y)

=∫dx f(x) ∇_{x}[-g'(x)]=∫dx f(x) [-g''(x)]

whereas if you take the other order:

I=∫∫dxdy ∇_{y}[∇_{x}δ(x-y)] f(x)g(y)

=∫∫dxdy g(y)∇_{y}[∇_{x}δ(x-y)] f(x)

=∫dx g(x) [-f''(x)]

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# Which order do you take derivative of delta function?

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