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  4. Find the derivative of ex +ey = ex+y

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Q. Find the derivative of $ e^{x} +e^{y} = e^{x+y} $

MHT CETMHT CET 2009

Solution:

$e^{x}+e^{y}=e^{x+y}=e^{x} e^{y} $
$\Rightarrow \,\,\, e^{-y}+e^{-x}=1$
On differentiating, we get
$-e^{-y} \frac{d y}{d x}+e^{-x}(-1)=0$
$\Rightarrow \,\,\, \frac{d y}{d x}=\frac{e^{-x}}{-e^{-y}}$
$\Rightarrow \,\,\, \frac{d y}{d x}=-e^{y-x}$