If e^x + e^y = e^{x + y}, prove that or, (CBSE 2014)

We are given with an equation e^x + e^y = e^{x + y}, we have to prove that by using the given equation we will first find the value of and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to x, we get,

e^x + e^y = e^{(x + y)} [1 + ]

[e^y – e^{x + y}] = e^{x + y} – e^x