Q. 165.0( 4 Votes )

If y=xsin x<

Answer :

Let u = xsin x


Taking log both sides,


log u = sin x log x


On differentiating,




Let, v = sin (xx)


Let, t = xx


log t = x log x


On differentiating,






Using (2),



As, y = u + v


So,


From (1) and (3),



OR


y = log (1 + 2t2 + t4)


Applying the formula (a + b)2 = a2 + b2 + 2ab in (1 + 2t2 + t4).


y = log (1+t2)2


As log xn = n log x


y = 2 log (1+t2)


On differentiating,



x = tan-1 t


On differentiating,



Now,


Again differentiating,



=4(1+t2)


Therefore,


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