JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y = {\log ^n}x

, where

{\log ^n}

means

\log \log \log \ldots

(repeated

n

times ),then

x\log x{\log ^2}x{\log ^3}x \ldots {\log ^{n - 1}}x{\log ^n}x\frac{{dy}}{{dx}}

is equal to

View answer and explanation

Correct option: D

{\log ^n}x

Option D (

{\log ^n}x

) is correct because after differentiating and rearranging, the expression simplifies to

{\log ^n}x

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x

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