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Partial differentiation -higher order

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    The determinant J (f,g/u,v) =|∂f/∂u ∂f/∂v

    ∂g/∂u ∂g/∂v |:

    if z = f(x,y) and g(x,y) = 0, show that dz/dx = ∂f/∂x*∂g/∂y - ∂f/∂y * ∂g/∂x/∂g/∂y = 1/ ∂g/∂yJ(f,g/x,y)

    2. Relevant equations

    ∂z/∂x = ∂z/∂f*∂f/∂x
    ∂z/∂x = ∂z/∂g*∂g/∂x
    ∂z/∂y = ∂z/∂f*∂f/∂y
    ∂z/∂y = ∂z/∂g*∂g/y

    3. The attempt at a solution

    should u be placed in the f function and v in the g function? So it may be f(u), g(v) = 0. need some tips please
  2. jcsd
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