If $f(x)=\log _x(\ln x)$, then at $x=e, f^{\prime}(x)$ equals-

JEE MATHEMATICS MCQ: TANGENTS & NORMALS

1 Easy

1 of 1

Application +4 | -1

f(x)=\log _x(\ln x)

, then at

x=e, f^{\prime}(x)

equals-

View answer and explanation

Correct option: D

1 / e

Option D (1/e) is correct because after applying the change of base formula and differentiating, the value of f'(e) is 1/e.

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a

y=x^3-a x

x^2 y=1-y

x y=1-y

C

y^3-3 x y+2=0

H

\mathrm{C}

x

V

C

y

y-e^{x y}+x=0

y = f\left( x \right)

x

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z