# What is the implicit derivative of 10=ye^y-x^2+ye^x ?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 x - y {e}^{x}}{\left(1 + y\right) {e}^{y} + {e}^{x}}$
Implicit differentiation of $10 = y {e}^{y} - {x}^{2} + y {e}^{x}$ is
$0 = \frac{\mathrm{dy}}{\mathrm{dx}} {e}^{y} + y {e}^{y} \frac{\mathrm{dy}}{\mathrm{dx}} - 2 x + \frac{\mathrm{dy}}{\mathrm{dx}} {e}^{x} + y {e}^{x}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 x - y {e}^{x}}{{e}^{y} + y {e}^{y} + {e}^{x}} = \frac{2 x - y {e}^{x}}{\left(1 + y\right) {e}^{y} + {e}^{x}}$