\[ {}y^{\prime } = \frac {\left (18 x^{\frac {3}{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{\frac {5}{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \]

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

\[ {}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \]

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \]

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

\[ {}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \]

\[ {}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \]

\[ {}y^{\prime } = \frac {-4 y a x -a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \]

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

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

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

\[ {}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \]

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

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

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

\[ {}y^{\prime } = \frac {\left (-x^{3} \sqrt {a}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \]

\[ {}y^{\prime } = \frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \]

\[ {}y^{\prime } = \frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \]

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

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

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

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

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