i need to use implicit differentiation to find the derivative:

Question

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?

Answer 1

yx+y = 8

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

(x+1)dy/dx = -y

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

Answer 2

Oddly, the answers agree, since

8 = y(x+1), so

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