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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \]

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

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

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

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

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

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

\[ {}y^{\prime } = -\frac {\left (\sqrt {a}\, x^{4}+x^{3} \sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \]

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

\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {y+x^{3} \ln \relax (x )+x^{4}+x^{3}+7 x y^{2} \ln \relax (x )+7 x^{2} y^{2}+7 x y^{2}}{x} \]

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {y \ln \relax (x ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (\ln \relax (x ) x -1\right ) x} \]

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

\[ {}y^{\prime } = -\frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \relax (x )\right ) x \left (y+1\right )^{2}}{8} \]

\[ {}y^{\prime } = \frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \relax (x )\right )^{2} x \left (y+1\right )^{2}}{16} \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \]

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

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

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

\[ {}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \]