DualState

The issue here is that the operation of derivation is not an equivalence tranformation. Equivalence transformations must be reversible, but reversing the derivation would be an integration. But the integration introduces an integration constant of which the actual value is unknown. So, by deriving and integrating one expression, we basically add a constant to it and have changed it. This is why the derivation is no equivalence tranformation and messes up our equation.

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