If yx + xy + xx = ab, find .
Given that, yx + xy + xx = ab
Putting, u=yx, v=xy, w=xx ,we get
u+v+w=ab
Therefore, ……(i)
Now, u=yx,
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,