Question

If e^x + e^y = e^{x + y}, prove that dy/dx + e^{y - x} = 0.

Answer 1

Given,

e^x + e^y = e^{x + y} .........(i)

On dividing Eq. (i) by e^{x + y} we get

e^-x + e^-y = 1 ..........(ii)

On differentiating both sides of Eq. (ii) w.r.t. x, we get

Hence proved