Question
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?
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?
Answers
yx+y = 8
y dx/dx + x dy/dx + dy/dx = 0
(x+1)dy/dx = -y
dy/dx = -y/(x+1)
y dx/dx + x dy/dx + dy/dx = 0
(x+1)dy/dx = -y
dy/dx = -y/(x+1)
Oddly, the answers agree, since
8 = y(x+1), so
-8/(x+1)^2 = -(8/(x+1))/(x+1) = -y/(x+1)
8 = y(x+1), so
-8/(x+1)^2 = -(8/(x+1))/(x+1) = -y/(x+1)
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