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Homework Help: Partial Derivative

  1. Dec 17, 2007 #1
    Whoops got it now, didn't carry out my substitutions far enough.

    1. The problem statement, all variables and given/known data
    [tex]
    z = x^2 + 2y^2
    [/tex]
    [tex]
    x = rcos(\theta)
    [/tex]
    [tex]
    y = rsin(\theta)
    [/tex]
    2. Relevant equations



    3. The attempt at a solution
    Find [tex](\partial z/\partial x)[/tex] (theta is constant)

    dz = 2xdx + 4ydy
    dx = cos[tex](\theta)[/tex]dr - rsin[tex](\theta)[/tex]d[tex]\theta[/tex]
    dy = sin[tex](\theta)[/tex]dr + rcos[tex](\theta)[/tex]d[tex]\theta[/tex]

    Unfortunately I'm not really quite sure where to go from here, I know that
    [tex](\frac{ \partial z } { \partial x} )[/tex] is 2x when y is constant. But how to factor in theta being constant?
    I suppose I could reduce
    dx to dx = cos[tex](\theta)[/tex]dr
    and dy = sin[tex](\theta)[/tex]dr
     
    Last edited: Dec 17, 2007
  2. jcsd
  3. Dec 17, 2007 #2

    HallsofIvy

    User Avatar
    Science Advisor

    If [itex]\theta[/itex] is a constant, then [itex]d\theta= 0[/itex]

    Yes, that is exactly correct. Then dz= dx+ dy= ?
     
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