Given: x^y + y^x = 1

Let y= x^y + y^x = 1

Let u = x^y and v = y^x

Then, ⇒ u + v = 1

For, u = x^y

Taking log on both sides, we get

Log u =log x^y

⇒log u = y.log(x)

Now, differentiate both sides with respect to x

For, v = y^x

Taking log on both sides, we get

Log v =log y^x

⇒log v = x.log(y)

Now, differentiate both sides with respect to x