\[ {}y^{\prime } = \frac {y \left (x y+1\right )}{x \left (-x y-1+y^{4} x^{3}\right )} \]

\[ {}y^{\prime } = \frac {\left (4 \,{\mathrm e}^{-x^{2}}-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}-4 x^{2} {\mathrm e}^{-x^{2}} y+x^{4} {\mathrm e}^{-2 x^{2}}\right ) x}{4} \]

\[ {}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \]

\[ {}y^{\prime } = \frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (-1+x \right ) \left (x +y\right )} \]

\[ {}y^{\prime } = \frac {\left (\left (x^{2}+1\right )^{\frac {3}{2}} x^{2}+\left (x^{2}+1\right )^{\frac {3}{2}}+y^{2} \left (x^{2}+1\right )^{\frac {3}{2}}+x^{2} y^{3}+y^{3}\right ) x}{\left (x^{2}+1\right )^{3}} \]

\[ {}y^{\prime } = \frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {-y+x^{3} \sqrt {x^{2}+y^{2}}-x^{2} \sqrt {x^{2}+y^{2}}\, y}{x} \]

\[ {}y^{\prime } = \frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x y^{3}+2 x y^{4}\right )} \]

\[ {}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \]

\[ {}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y-y^{3}-y^{4}\right )} \]

\[ {}y^{\prime } = \frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \]

\[ {}y^{\prime } = \frac {\left (1+x +y\right ) y}{\left (y^{4}+y^{3}+y^{2}+x \right ) \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {-y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y}{x} \]

\[ {}y^{\prime } = \frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{\frac {2}{3}} x -f_{1}\left (y^{3}-3 \ln \relax (x )\right ) \left (y^{3}\right )^{\frac {1}{3}} x} \]

\[ {}y^{\prime } = \frac {y \left (x -y\right ) \left (y+1\right )}{x \left (x y+x -y\right )} \]

\[ {}y^{\prime } = -\frac {1}{-\ln \relax (x ) \left (y^{3}\right )^{\frac {2}{3}}-f_{1}\left (y^{3}+3 \expIntegral \left (1, -\ln \relax (x )\right )\right ) \ln \relax (x ) \left (y^{3}\right )^{\frac {1}{3}}} \]

\[ {}y^{\prime } = \frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{\frac {7}{2}}+100 x}{25 x} \]

\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \]

\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \]

\[ {}y^{\prime } = \frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{\frac {3}{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{\frac {3}{2}} b \,x^{2}+a^{\frac {5}{2}} y^{4}}{a \,x^{2} y} \]

\[ {}y^{\prime } = \frac {y+x^{2} \ln \relax (x )^{3}+2 x^{2} \ln \relax (x )^{2} y+x^{2} \ln \relax (x ) y^{2}}{x \ln \relax (x )} \]

\[ {}y^{\prime } = \frac {y+x^{3} \ln \relax (x )^{3}+2 x^{3} \ln \relax (x )^{2} y+x^{3} \ln \relax (x ) y^{2}}{x \ln \relax (x )} \]

\[ {}y^{\prime } = \frac {y \left (x +y\right ) \left (y+1\right )}{x \left (x y+x +y\right )} \]

\[ {}y^{\prime } = \frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \]

\[ {}y^{\prime } = \frac {1}{-x +\left (\frac {1}{y}+1\right ) x +f_{1}\left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-f_{1}\left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \]

\[ {}y^{\prime } = \frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \]

\[ {}y^{\prime } = \frac {\cosh \relax (x )}{\sinh \relax (x )}+f_{1}\left (y-\ln \left (\sinh \relax (x )\right )\right ) \]

\[ {}y^{\prime } = -\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \]

\[ {}y^{\prime } = \frac {1}{\sin \relax (x )}+f_{1}\left (y-\ln \left (\sin \relax (x )\right )+\ln \left (\cos \relax (x )+1\right )\right ) \]

\[ {}y^{\prime } = \frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}} \]

\[ {}y^{\prime } = \frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \]

\[ {}y^{\prime } = \frac {14 x y+12+2 x +x^{3} y^{3}+6 x^{2} y^{2}}{x^{2} \left (x y+2+x \right )} \]

\[ {}y^{\prime } = \frac {y \left (\ln \relax (x )+\ln \relax (y)-1+x^{2} \ln \relax (x )^{2}+2 x^{2} \ln \relax (y) \ln \relax (x )+x^{2} \ln \relax (y)^{2}\right )}{x} \]

\[ {}y^{\prime } = \frac {y \left (\ln \relax (y)-1+\ln \relax (x )+\ln \relax (x )^{2} x^{3}+2 x^{3} \ln \relax (y) \ln \relax (x )+x^{3} \ln \relax (y)^{2}\right )}{x} \]

\[ {}y^{\prime } = -\frac {\left (-\frac {1}{x}-f_{1}\left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \]

\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \]

\[ {}y^{\prime } = \frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+y^{3} a^{3}+3 y^{2} a^{2} b x +3 y a \,b^{2} x^{2}+b^{3} x^{3}}{a^{3}} \]

\[ {}y^{\prime } = -\frac {-x -f_{1}\left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \]

\[ {}y^{\prime } = \frac {-\sin \left (2 y\right )+x \cos \left (2 y\right )+\cos \left (2 y\right ) x^{3}+\cos \left (2 y\right ) x^{4}+x +x^{3}+x^{4}}{2 x} \]

\[ {}y^{\prime } = -\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-f_{1}\left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]

\[ {}y^{\prime } = -\left (\frac {\expIntegral \left (1, -\ln \left (y-1\right )\right )}{x}-f_{1}\relax (x )\right ) \ln \left (y-1\right ) \]

\[ {}y^{\prime } = \frac {y+x \sqrt {x^{2}+y^{2}}+x^{3} \sqrt {x^{2}+y^{2}}+x^{4} \sqrt {x^{2}+y^{2}}}{x} \]

\[ {}y^{\prime } = \frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \]

\[ {}y^{\prime } = \left (\frac {\ln \left (y-1\right ) y}{\left (1-y\right ) \ln \relax (x ) x}-\frac {\ln \left (y-1\right )}{\left (1-y\right ) \ln \relax (x ) x}-f \relax (x )\right ) \left (1-y\right ) \]

\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \]

\[ {}y^{\prime } = -\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27} \]

\[ {}y^{\prime } = 2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 x^{2} y^{2}+3 y x^{4}-x^{6} \]

\[ {}y^{\prime } = \frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \]

\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \]

\[ {}y^{\prime } = \frac {2 x y^{2}+4 y \ln \left (1+2 x \right ) x +2 \ln \left (1+2 x \right )^{2} x +y^{2}-2+\ln \left (1+2 x \right )^{2}+2 y \ln \left (1+2 x \right )}{1+2 x} \]

\[ {}y^{\prime } = \frac {-30 x^{3} y+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \]

\[ {}y^{\prime } = \frac {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 x y+2 x y^{4}\right )} \]

\[ {}y^{\prime } = \frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \]

\[ {}y^{\prime } = -\frac {-x y-y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {y^{2} \left (x^{2} y-2 x -2 x y+y\right )}{2 \left (-2+x y-2 y\right ) x} \]

\[ {}y^{\prime } = \frac {-2 x y+2 x^{3}-2 x -y^{3}+3 x^{2} y^{2}-3 y x^{4}+x^{6}}{-y+x^{2}-1} \]

\[ {}y^{\prime } = \frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \]

\[ {}y^{\prime } = -\frac {-x y-y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y}{x \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

\[ {}y^{\prime } = \frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27} \]

\[ {}y^{\prime } = -\frac {\left (-108 x^{\frac {3}{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{216} \]

\[ {}y^{\prime } = \frac {\left (a^{3}+y^{4} a^{3}+2 y^{2} a^{2} b \,x^{2}+a \,x^{4} b^{2}+y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{\frac {7}{2}} y} \]

\[ {}y^{\prime } = -\frac {\left (-1-y^{4}+2 x^{2} y^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 x^{4} y^{2}+x^{6}\right ) x}{y} \]

\[ {}y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \]

\[ {}y^{\prime } = \frac {2 x^{2}-4 x^{3} y+1+x^{4} y^{2}+x^{6} y^{3}-3 y^{2} x^{5}+3 y x^{4}-x^{3}}{x^{4}} \]

\[ {}y^{\prime } = \frac {y a^{2} x +a +a^{2} x +y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 y a x +1}{a^{2} x^{2} \left (y a x +1+a x \right )} \]

\[ {}y^{\prime } = \frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \]

\[ {}y^{\prime } = -\frac {\left (-8-8 y^{3}+24 y^{\frac {3}{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{\frac {9}{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{\frac {3}{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \]

\[ {}y^{\prime } = \frac {x}{-y+1+y^{4}+2 x^{2} y^{2}+x^{4}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \]

\[ {}y^{\prime } = \frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+y x^{4}\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \]

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}} \]

\[ {}y^{\prime } = \frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8}{x^{3}} \]

\[ {}y^{\prime } = -\frac {i \left (i x +1+x^{4}+2 x^{2} y^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+y^{6}\right )}{y} \]

\[ {}y^{\prime } = \frac {\left (-256 x^{2} a y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \]

\[ {}y^{\prime } = \frac {x +1+y^{4}-2 x^{2} y^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 x^{4} y^{2}-x^{6}}{y} \]

\[ {}y^{\prime } = \frac {\left (-108 y x^{\frac {3}{2}}+18 x^{\frac {9}{2}}-108 x^{\frac {3}{2}}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \]

\[ {}y^{\prime } = \frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \]

\[ {}y^{\prime } = \frac {32 x^{5}+64 x^{6}+64 y^{2} x^{6}+32 y x^{4}+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}} \]

\[ {}y^{\prime } = \frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 y a x -y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \]

\[ {}y^{\prime } = \frac {\left (y-a \ln \relax (y) x +x^{2}\right ) y}{\left (-y \ln \relax (y)-y \ln \relax (x )-y+a x \right ) x} \]

\[ {}y^{\prime } = \frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 x^{4} y^{2}+x^{6}}{\left (-y^{2}+x^{2}-1\right ) y} \]

\[ {}y^{\prime } = \frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \]

\[ {}y^{\prime } = \frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \]

\[ {}y^{\prime } = \frac {a^{2} x +a^{3} x^{3}+a^{3} x^{3} y^{2}+2 a^{2} x^{2} y+a x +y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 y a x +1}{a^{3} x^{3}} \]

\[ {}y^{\prime } = \frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \]

\[ {}y^{\prime } = \frac {-2 \cos \relax (x ) x +2 \sin \relax (x ) x^{2}+2 x +2 y^{2}+4 y \cos \relax (x ) x -4 x y+x^{2} \cos \left (2 x \right )+3 x^{2}-4 x^{2} \cos \relax (x )}{2 x} \]

\[ {}y^{\prime } = \frac {4 x \left (a -1\right ) \left (a +1\right )}{4 y+a^{2} y^{4}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 x^{2} y^{2}-x^{4}} \]

\[ {}y^{\prime } = \frac {x^{3}+y^{4} x^{3}+2 x^{2} y^{2}+x +x^{3} y^{6}+3 x^{2} y^{4}+3 x y^{2}+1}{x^{5} y} \]

\[ {}y^{\prime } = \frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x} \]

\[ {}y^{\prime } = -\left (-\frac {\ln \relax (y)}{x}+\frac {\cos \relax (x ) \ln \relax (y)}{\sin \relax (x )}-f_{1}\relax (x )\right ) y \]

\[ {}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

\[ {}y^{\prime } = -\frac {-y^{3}-y+2 y^{2} \ln \relax (x )-\ln \relax (x )^{2} y^{3}-1+3 y \ln \relax (x )-3 \ln \relax (x )^{2} y^{2}+\ln \relax (x )^{3} y^{3}}{y x} \]

\[ {}y^{\prime } = \frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 x^{2} a y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

\[ {}y^{\prime } = -\frac {-y^{3}-y+4 y^{2} \ln \relax (x )-4 \ln \relax (x )^{2} y^{3}-1+6 y \ln \relax (x )-12 \ln \relax (x )^{2} y^{2}+8 \ln \relax (x )^{3} y^{3}}{y x} \]

\[ {}y^{\prime } = \frac {y \left (\ln \relax (y) x +\ln \relax (y)-x -1+x \ln \relax (x )+\ln \relax (x )+x^{4} \ln \relax (x )^{2}+2 x^{4} \ln \relax (y) \ln \relax (x )+x^{4} \ln \relax (y)^{2}\right )}{x \left (1+x \right )} \]

\[ {}y^{\prime } = \frac {y \left (x \ln \relax (x )+\ln \relax (x )+\ln \relax (y) x +\ln \relax (y)-x -1+x \ln \relax (x )^{2}+2 x \ln \relax (y) \ln \relax (x )+x \ln \relax (y)^{2}\right )}{x \left (1+x \right )} \]

\[ {}y^{\prime } = \frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 x y^{4}+32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \]

\[ {}y^{\prime } = \frac {y^{\frac {3}{2}} \left (x -y+\sqrt {y}\right )}{y^{\frac {3}{2}} x -y^{\frac {5}{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \]

\[ {}y^{\prime } = \frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \]