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Q.

If y=(log⁡x  )x then dydx=

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a

(logx)xlog(logx)+1logx

b

(logx)xlog(logx)−1logx

c

−(logx)xlog(logx)+1logx

d

−(logx)xlog(logx)−1logx

answer is A.

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Detailed Solution

y=(log⁡x)xlog⁡y=log⁡(log⁡x)x1ydydx=log⁡(log⁡x)+x1log⁡xddxlog⁡x=log⁡(log⁡x)+xlog⁡x1xdydx=ylog⁡(log⁡x)+1log⁡x
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