Question:
If $f(x)=\log _{e}\left(\log _{e} x\right)$, then write the value of $f^{\prime}(e)$.
Solution:
$f(x)=\log _{e}\left(\log _{e} x\right)$
Using the Chain Rule of Differentiation,
$f(x)=\frac{1}{\log _{e} x} \cdot \frac{1}{x}$
So, $f(e)=\frac{1}{\log _{e} e} \cdot \frac{1}{e}$
$=\frac{1}{e}$ (Ans)
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