# Given ye^x - x - y^2 = 0 calculate dy/dx ?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1 - {e}^{x} y}{{e}^{x} - 2 y}$
Calling $f \left(x , y\right) = y {e}^{x} - x - {y}^{2} = 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - {f}_{x} / \left({f}_{y}\right) = - \frac{{e}^{x} y - 1}{{e}^{x} - 2 y}$