Question

Find $\frac{dy}{dx}$ if $e^x+e^y=e^{x-y}$

Answer 1

Given

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

Differentiate on both sides w.r.t x

$e^x+e^y\frac{dy}{dx}=e^{x-y}(1-\frac{dy}{dx})$

$e^{x-y}-e^x=(e^y+e^{x-y})\frac{dy}{dx}$

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