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


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