Use implicit differentiation to find the derivative of y with reapect to x

Question

x^2y-y^2+ln(xy)=1

Answer 1

x^2 dy+2xydx - 2ydy +(1/xy)(xdy+ydx) = 0

[x^2-2y+1/y]dy + [2xy+1/x]dx = 0

dy/dx = -[2xy+1/x] / [x^2-2y+1/y]

Answer 2

Or, rearranging things a bit,

-y(2x^2y+1) / x(x^2y-2y^2+1)
= -y(2x^2y+1) / x(x^2y-y^2-1 + 2-y^2)
= y(2x^2y+1) / x(2-y^2+ln(xy))

Answer 3

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