Question

implicit differentiation.. x^2 - 2xy + y^2 - 6x + 2y=0

Answer 1

the answer is dy/dx = x-y-3/x-y-1.. it was written on the book

Answer 2

\[
-2 x y'(x)+2 y(x) y'(x)+2 y'(x)-2 y(x)+2 x-6=0
\]
Solve for y'(x) and you are done

Answer 3

\[
-2 \left(x y'(x)-y(x) y'(x)-y'(x)+y(x)-x+3\right)=0\\
x y'(x)-y(x) y'(x)-y'(x)+y(x)-x+3=0\\
x y'(x)-y(x) y'(x)-y'(x)=-y(x)+x-3\\
y'(x)( x -y(x) -1)=-y(x)+x-3\\
y'(x)=\frac{-y(x)+x-3}{-y(x)+x-1}

\]

Answer 4

yay thank you so much @eliassaab

Answer 5

YW @silverxx