Q. Find the derivative of $y\$ with respect to $x\$if $e^{x} + e^{y} = e^{x + y}$
A) $- e^{x - y}$
B) $e^{x - y}$
C) $- e^{y - x}$
D) $e^{y - x}$
Explanation
(c)
$e^{x} + e^{y} = e^{x + y} = e^{x}e^{y}$
$\Rightarrow \ e^{- y} + e^{- x} = 1$
On differentiating, we get
$- e^{- y}\frac{dy}{dx} + e^{- x}( - 1) = 0$
$\Rightarrow \ \ \frac{dy}{dx} = \frac{e^{- x}}{- e^{- y}} \Rightarrow \frac{dy}{dx} = - e^{y - x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.