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I doubt that he would ask us to derive the zero, first, second, and half life equations since they are given on the equation sheet. It probably wouldn't hurt to be able to go from the given rate laws to the integrated rate laws though.
We do not need to know how to, since the integrated rate laws will be provided on the formula sheet. However, according to my TA, it may be useful to memorize other helpful forms of these laws that do not appear on the formula sheet.
It is provided on your equation sheet but it is useful to know how to derive the half life ones since let's say you are asked to find the how much time it takes for the concentration to be 1/15 initial, you would first need to derive an equation for that (exactly the way you do for half life) then solve
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