Introduction to Polymers - Lecture 5.9 - Step growth molecular weight, part 6

Weight average molecular weight and polydispersity.
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I have a problem with these theories of calculating the Mw and Mn , only because as you regularly mention , P is a constant , how can we calculate the derivative of a variable that is constant. See I know that P is not constant , because it's obviously a function of time , temperature, heat , condition , monomer , and .... I understand that , but how can we factor P from its own function( P to the power of i) if its not a constant (as you always mention it is) and how can a constant variable have a derivative other than 0 ?