# How do you differentiate 1=(xy)/(e^x+xy)?

Nov 16, 2016

There is no derivative since the domain is empty.

#### Explanation:

Given:

$1 = \frac{x y}{{e}^{x} + x y}$

Multiply both sides by ${e}^{x} + x y$ to get:

${e}^{x} + x y = x y$

Subtract $x y$ from both sides to get:

${e}^{x} = 0$

There is no value of $x$ which satisfies this and so the domain is empty.