(1)
x^2+y^2-2xy =8
2x+2y.y' -2( xy'+y) =0
x+y.y' -( xy'+y) =0
(x-y)y' = x-y
y' =1
(2)
y^2 -4axy +b=0
2y.y' -4a(xy'+y) =0
y.y' -2a(xy'+y) =0
(y-2ax)y' =2ay
y' =2ay/(y-2ax)
(3)
y= x^2+lny
y'= 2x + (1/y)y'
yy'= 2xy + y'
(y-1)y' =2xy
y' =2xy/(y-1)
(4)
e^(x+y) =y^2
(1+y').e^(x+y) =2y.y'
[e^(x+y)-2y]y' = e^(x+y)
y' = e^(x+y)/[e^(x+y)-2y]
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