Answer :

Given: (log x)x + xlog x

Let y= (log x)x + xlog x


Let y = u + v


u = (log x)x and v = xlog x


For, u =(log x)x


Taking log on both sides, we get


log u =log (log x)x


log u = x.log (log(x))


Now, differentiate both sides with respect to x








For, v = xlog x


Taking log on both sides, we get


log v =log( xlog x)


log v = log x. log x


Now, differentiate both sides with respect to x







Because, y = u + v




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