If y^x + x^y + x^x = a^b, find .

Given that, y^x + x^y + x^x = a^b

Putting, u=y^x, v=x^y, w=x^x ,we get

u+v+w=a^b

Therefore, ……(i)

Now, u=y^x,

Taking log on both sides, we have

log u = x log y

Differentiating both sides with respect to x, we have

So,

……(ii)

Also, v=,

Taking log on both sides, we have

log v = y log x

Differentiating both sides with respect to x, we have

So,

……(iii)

Again, w=,

Taking log on both sides, we have

log w = x log x

Differentiating both sides with respect to x, we have

So,

……(iv)

From (i), (ii), (iii), (iv)

Therefore,