y`=?

[Гост]

y=y(x) зададено с у-то xe^{y}+ye^{x}-e^{xy}
y`=?

[aifC]

[tex]y' = 1e^{y} + ye^{x} - e^{yx} \cdot (yx)' = -y \cdot (x)' \cdot e^{xy} + ye^{x} + e^{y} = -1ey^{yx} + ye^{x} + e^{y} = -ye^{yx} + ye^{x} + e^{y};[/tex]

[Добромир Глухаров]

$F(x,y)=xe^y+ye^x-e^{xy}=0$

$\frac{d}{dx}F(x,y)=0$

$F'_x(x,y).x'_x+F'_y(x,y).y'_x=0$

$y'_x=-\frac{F'_x}{F'_y}=-\frac{e^y+ye^x-ye^{xy}}{xe^y+e^x-xe^{xy}}$