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![xy(x+y)=0\\\\
\textit{derivemos:}\\ \\
\left[xy(x+y)\right]'=0\\\\
(xy)'(x+y)+xy(x+y)'=0\\ \\
(y+xy')(x+y)+xy(1+y')=0\\ \\
xy+y^2+x^2y'+xyy'+xy+xyy'=0 \\ \\
(x^2+y+2xy)y' = -2xy-y^2\\ \\
\boxed{y'=-\dfrac{2xy+y^2}{x^2+y+2xy}}](https://tex.z-dn.net/?f=xy%28x%2By%29%3D0%5C%5C%5C%5C%0A%5Ctextit%7Bderivemos%3A%7D%5C%5C+%5C%5C%0A%5Cleft%5Bxy%28x%2By%29%5Cright%5D%27%3D0%5C%5C%5C%5C%0A%28xy%29%27%28x%2By%29%2Bxy%28x%2By%29%27%3D0%5C%5C+%5C%5C%0A%28y%2Bxy%27%29%28x%2By%29%2Bxy%281%2By%27%29%3D0%5C%5C+%5C%5C%0Axy%2By%5E2%2Bx%5E2y%27%2Bxyy%27%2Bxy%2Bxyy%27%3D0+%5C%5C+%5C%5C%0A%28x%5E2%2By%2B2xy%29y%27+%3D+-2xy-y%5E2%5C%5C+%5C%5C%0A%5Cboxed%7By%27%3D-%5Cdfrac%7B2xy%2By%5E2%7D%7Bx%5E2%2By%2B2xy%7D%7D%0A "xy(x+y)=0\\\\
\textit{derivemos:}\\ \\
\left[xy(x+y)\right]'=0\\\\
(xy)'(x+y)+xy(x+y)'=0\\ \\
(y+xy')(x+y)+xy(1+y')=0\\ \\
xy+y^2+x^2y'+xyy'+xy+xyy'=0 \\ \\
(x^2+y+2xy)y' = -2xy-y^2\\ \\
\boxed{y'=-\dfrac{2xy+y^2}{x^2+y+2xy}}")
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