1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proof Involving an Implicity Defined Multivariable Function

  1. Sep 26, 2008 #1
    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
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted