Answer :

Given that f(x) = |log_{e} x| where

Clearly f(x) is differentiable for x>1 and x<1. So, we will check the differentiability at x = 1.

LHD at x =1,

RHD at x =1,

∵ LHD ≠RHD

∴ f(x) = |log_{e} x| is not differentiable.

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