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Homework Help: Partial Derivatives

  1. Nov 5, 2012 #1
    Find the two first-order partial derivatives of z with respect to x and y
    when z = z(x, y) is defined implicitly by


    I started by multiplying the brackets out to give; ze^xy + zy + z^3 - 1 = 0

    i then differentiated each side implicitly and got;
    dz/dx = yze^xy
    dz/dy = xze^xy + z

    I'm happy with dz/dx but i've gone wrong on the dz/dy and i don't know where.
  2. jcsd
  3. Nov 5, 2012 #2


    Staff: Mentor

    Show us what you got for ## \frac{\partial z}{\partial y}##

    I suspect that when you differentiated zy you neglected to use the product rule, or when you differentiated z3, you didn't use the chain rule.
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