# How do you implicitly differentiate 22=(x)/(1-xe^y)?

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1 + 22 {e}^{y}}{22 x {e}^{y}}$
Using cross multiplication it is, $22 - 22 x {e}^{y} = x$.
Now differentiate w.r.t x, $0 - 22 {e}^{y} - 22 x {e}^{y} \frac{\mathrm{dy}}{\mathrm{dx}} = 1$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1 + 22 {e}^{y}}{22 x {e}^{y}}$