# How do you implicitly differentiate y= (x-y) e^(xy)-xy^2 ?

Jun 5, 2018

$y ' = \frac{{e}^{x y} + y \left(x - y\right) {e}^{x y} - {y}^{2}}{1 + {e}^{x y} - x \left(x - y\right) {e}^{x y} + 2 x y}$

#### Explanation:

Differentiating with respect to $x$

$y ' = \left(1 - y '\right) {e}^{x y} + \left(x - y\right) {e}^{x y} \left(y + x y '\right) - {y}^{2} - 2 x y y '$
so we get
$y ' \left(1 + {e}^{x y} - x \left(x - y\right) {e}^{x y} + 2 x y\right) = {e}^{x y} + y \left(x - y\right) {e}^{x y} - {y}^{2}$