If $e^{x} + e^{y} = 1$, what is $\frac{dy}{dx}$?

Explanation

1. 01

   $e^{x} + e^{y}\frac{dy}{dx} = 0$.

2. 02

   $\frac{dy}{dx} = -\frac{e^{x}}{e^{y}} = -e^{x - y}$.