Answer :

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,



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