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: Multivariate Chain Rule

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex] \frac{\partial z}{\partial y} [/itex]
    where z=F(u,v,y), u=f(v,x), v=g(x,y).

    3. The attempt at a solution
    If I remember multivariate calculus at all, this should be (please forgive the abuse of notation)

    [tex] \frac{\partial z}{\partial y} = \frac{\partial z}{\partial u}\frac{\partial u}{\partial v}\frac{\partial v}{\partial y} + \frac{\partial z}{\partial v}\frac{\partial v}{\partial y} + \frac{\partial z}{\partial y} [/tex]

    However, I have a book in front of me that says it should be

    [tex] \frac{\partial z}{\partial y} = \frac{\partial z}{\partial v}\frac{\partial v}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial z}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial z}{\partial y} [/tex]

    I think I'm correct and that they must have confused u and v. If someone could verify this for me it would be much appreciated.
  2. jcsd
  3. Jul 21, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    I agree. It think they mixed up u and v.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook