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I'm trying to do the following variational operation in Mathmatica and VariationalD command doesn't give me the correct answer. Is there any other command that I am unaware of ? $\delta (y'' * y) = \delta y'' * y + \delta y * y''$

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D[y'' y /. y -> y + s δy, s] /. s -> 0

δy y^′′ + y δy^′′

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