Question

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).".