Q. 34.0( 4 Votes )

Differentiate (lo

Answer :

Let u = (log x)x and v = log x.


We need to differentiate u with respect to v that is find.


We have u = (log x)x


Taking log on both sides, we get


log u = log(log x)x


log u = x × log(log x) [ log am = m × log a]


On differentiating both the sides with respect to x, we get



Recall that (uv)’ = vu’ + uv’ (product rule)



We know and




But, u = (log x)x and





Now, on differentiating v with respect to x, we get




We have







Thus,


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