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In order to understand the integrated rate law it is important to know where it came from, but I doubt Dr. Lavelle would ask us to specifically derive one equation from the other. If anything, developing an understanding of the relationship fosters a clearer understanding of reaction kinetics, though!
I think we should be ready for anything. We've spent a lot of time in class on derivations and integrations, so I wouldn't be surprised if he asks us to derive something at some point. It shows a true understanding of the material, and is something that could only be helpful to know!
Although Dr. Lavelle does a lot of derivations in class, I believe he does them so we can see the correlations. I doubt we would be asked to derive the integrated rate law since practical application seems to be more the theme of his exams
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