Question

If $e^x+e^y=e^{x+y},$ then $\frac{dy}{dx}=$

• A. $-e^{x-y}$
• B. $e^{x-y}$
• C. $-e^{y-x}$
• D. $e^{y-x}$

Answer 1

The correct option is C $-e^{y-x}$

Given,
$e^x+e^y=e^{x+y}=e^x{e}^y$
$\Rightarrow e^{-y}+e^{-x}=1$
Differentiating both sides with respect to $x$, we get
$-e^{-y}\frac{dy}{dx}-e^{-x}=0$
$\Rightarrow \frac{dy}{dx}=\frac{e^{-x}}{-e^{-y}}$
$\Rightarrow \frac{dy}{dx}=-e^{y-x}$