(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that the equation G(s, t, u) = 0 implicitly defines each of the three variables s, t, and u as

functions of the other two: s = x(t, u), t = y(s, u), and u = z(s, t). If G is differentiable and Gs,

Gt, and Gu are all nonzero, show that

1 = - (δu/δs) · (δs/δt) · (δt/δu)

2. Relevant equations

δz/δs = δz/δx · δx/δs + δz/δy · δy/δs

δz/δt = δz/δx · δx/δt + δz/δy · δy/δt

3. The attempt at a solution

δG/δs = δG/δs * δs/δt + δG/δs * δs/δu

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# Homework Help: Proof Involving an Implicity Defined Multivariable Function

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