How to reach 1st, 2nd, 3rd order and the rate law

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Please explain how to reach 1st, 2nd, 3rd order and the rate law: What do they mean? How do I reach them? Differential, not integrated).

Solution: The rate of a chemical reaction dictates whether a reaction can occur during a lifetime. Knowing the rate law, an expression relating the rate to the concentrations of reactants, can help a chemist adjust the reaction conditions to get a more suitable rate.

Rate is the speed of a ...