Answer :

Let xx = u and yx = v


Taking log on both sides we get,


x log x = log u ……(1),


x log y = log v ……(2)


Using


Differentiating both sides of equation (1) we get,




Differentiating both sides of equation (2) we get,




We know that, from question,


u + v = 1


Differentiating both sides we get,



Putinng the value of eq(4) and eq(5) in equation above we get,





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