Question

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

Answer 1

Given,

e^x + e^y = e^{x + y}

Dividing Eq. (i) by e^{x + y}, we get

e^-y + e^-x = 1 …(ii)

Differentiating both sides of Eq. (ii) w.r.t.’x’, we get