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## Main Question or Discussion Point

I know this is a simple question, but if I take the derivative of the left hand side, do I have to take the derivative of the right hand side? How do I maintain equality with the derivative? it's not an algebraic operation, so I'm not sure if I can just do the same thing to both sides and it still be equal.

what about integration? for integration, if I have to take the integral of both sides, how do I pick my bounds?

what about integration? for integration, if I have to take the integral of both sides, how do I pick my bounds?