Integrate[DiracDelta'[y - z] DiracDelta[x - z], {z, -Infinity, Infinity},
Assumptions -> x \[Element] Reals && x \[Element] Reals]
Integrate[DiracDelta'[y - z] DiracDelta[x - z], {z, -Infinity, Infinity},
Assumptions -> x \[Element] Reals && x \[Element] Reals]
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