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The differential rate law provides the relationship between the rate of a reaction and the concentration of the reactant. This determines the dependence of a reaction on the concentration of a specific reactant by giving the contribution of each reactant to the overall rate of the reaction.
And I think that differential rate law is actually the source of integrated rate law (obtained by integrating the differential rate law on both sides). Also, differential rate law could give the plot of rate versus time.
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