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Another implicit differentiation question

  1. Oct 8, 2006 #1
    ok so i did this problem but i wasnt sure if this is correct.

    y = 8x + 5cos(xy) + 7

    dy/dx = 8 + 5(-sin xy)(x dy/dx + y)
    dy/dx = 8 - (5x) (sin xy) dy/dx - (5y) (sin xy)
    (5x) (sin xy) dy/dx + dy/dx = 8 - (5y) (sin xy)
    [(5x) (sin xy) + 1] dy/dx = 8 - (5y) (sin xy)
    dy/dx = [8 - (5y) (sin xy)]/[(5x) (sin xy) + 1]

    does that look right?
  2. jcsd
  3. Oct 8, 2006 #2
    Looks fine. I don't see any errors.

    I wish I could show you via this forum how to "think" to go from the first line to the last line without any of the in-between steps.

    Maybe you can figure it out from this: you know that you're going to get all the dy/dx terms on one side and then factor out dy/dx later. So, the numerator simply becomes all the non dy/dx terms, and the denominator becomes what's left. Minor attention to signs, and you save a LOT of writing.
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