Continuity and DifferentiabilityHard
Question
If y = x(lnx)ln ln x, then 
is equal to :
is equal to :Options
A.
(2 ln ln x + 1)
(2 ln ln x + 1)B.
(2 ln ln x + 1)
(2 ln ln x + 1)C.
(2 ln ln x + 1)
(2 ln ln x + 1)D. None of these
Solution
y = x(lnx)ln ln x .......(i)
taking loge both sides, we get
lny = (ln x)ln (ln x) . lnx
Again taking loge , we get
ln (ln y) = ln (ln x) . ln (ln x) + ln (ln x)
= {ln (ln x)} [ln (ln x) + 1]
Diff. w.r.t. x,
[ln (ln x) + 1] + {ln (ln x)} 
⇒
= y lny 
⇒
= y lny 
taking loge both sides, we get
lny = (ln x)ln (ln x) . lnx
Again taking loge , we get
ln (ln y) = ln (ln x) . ln (ln x) + ln (ln x)
= {ln (ln x)} [ln (ln x) + 1]
Diff. w.r.t. x,
[ln (ln x) + 1] + {ln (ln x)} ⇒
= y lny ⇒
= y lny Create a free account to view solution
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