calculus

i need to use implicit differentiation to find the derivative:
yx+y = 8

i keep getting y'=-1-y.

i already know the derivative of this, by using explicit by simplification:

y(x+1)=8
y=(8)/(x+1)
y'= -(8)/(x+1)^2

how do i go about doing this the right way?

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asked by eric
  1. yx+y = 8

    y dx/dx + x dy/dx + dy/dx = 0

    (x+1)dy/dx = -y

    dy/dx = -y/(x+1)

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    posted by Damon
  2. Oddly, the answers agree, since

    8 = y(x+1), so

    -8/(x+1)^2 = -(8/(x+1))/(x+1) = -y/(x+1)

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    posted by Steve

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