Question

If $e^{x} +e^{y} = e^{x+y}$, show that $\frac{dy}{dx}= -e^{y-x}$

Answer 1

hey mate
here's the solution

Answer 2

hey buddy here's ur answer,,,

Answer:

dydx=e^x(e^y−1)e^y(1−e^x)

Explanation:

Differentiating e^x+e^y=e^x+y

e^x+e^ydydx=e^x+y(1+dydx)

or e^x+e^ydydx=e^x+y+e^x+ydydx

or e^ydydx−e^x+ydydx=e^x+y−e^x

or (e^y−e^x+y)dydx=(e^x+y−e^x)

or dydx=e^x+y−e^xe^y−e^x+y=e^x(e^y−1)e^y(1−e^x)


hope it helps u buddy⏩⏩⏩