When I'm setting up the equations for $∂P1/∂Pn$, I first have 1. P1=1/(P2....Pn) and next 2. P1=1-P2-...Pn. Partially differentiating both with respect to Pn gives me -1/(P2....Pn-1)*1/(Pn)^2 for the first equation and 1 for the second equation. I'm confused on how I can get one single answer for ∂*P*1/∂*Pn. *I'm also confused about what it means when it says "Consider these 2 relations to implicitly determine the first 2 numbers as functions of the others, p1 = p1(p3,p4,...,pn), p2 = p2(p3,p4,...,pn).".

Image transcriptions

2. Consider n numbers p1, p2, . ..,Pn which both multiply and add to give 1: PIP2 . . . Pn = 1, Pi + p2 + . . . + Pn = 1. Consider these 2 relations to implicitly determine the first 2 numbers as functions of the others, p1 = p1 (P3, PA, . . ., Pn), P2 = P2 (P3, PA, . . .,Pn). Compute 921 (in terms of PI , P2, . . . , Pn).

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