\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {-3\,{x}^{2}y \left( x \right) -2\,{x}^{3}-2\,x-x \left( y \left( x \right)  \right) ^{2}-y \left( x \right) +{x}^{3} \left( y \left( x \right)  \right) ^{3}+3\,{x}^{4} \left( y \left( x \right)  \right) ^{2}+3\,{x}^{5}y \left( x \right) +{x}^{6}}{x \left( xy \left( x \right) +{x}^{2}+1 \right) }}=0}
\]