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## Homework Statement

Hi,I saw a statement in my physics notes like this(Anyway it is a maths problem):

where L is a general differential operator.G is a green's function(I guess it is irrelevant)

My question is related to the red line:

Suppose we have this:

∂/∂x ∫ f(x-y)g(y) ∂y

is it generally true that

∂/∂x ∫ f(x-y)g(y) ∂y = ∫ ∂/∂x [ f(x-y)g(y) ] ∂y ?

## Homework Equations

Please answer it as simply as you can...Since I have not done multivariable calculus...(Though I would be happy to check it out if there is a theorem related to this.)

## The Attempt at a Solution

If the above is simplified to ∂/∂x ∫ f(x)g(y) ∂y ,then ∂/∂x [f(x) ∫ g(y) ∂y]

⇒ ∫ ∂/∂x [ f(x) ] g(y) ∂y

⇒ ∫ ∂/∂x [ f(x)g(y) ] ∂y

But I dont know what to do with the (x-y) term..

Thanks