Find derivative of x with respect to y

Question

e^x+e^y=e^x+y

Answer 1

Given,

e^x + e^y = e^x+y = e^xe^y

⇒ e^−y + e^−x = 1

Differentiating both sides with respect to x, we get

\(-e^{-y} \frac{dy}{dx} - e^{-x} = 0\)

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

⇒ \(\frac{dy}{dx} = -e^{y-x}\)