જો f(x) = _x ( x), તો f'(x) એ x = e આગળ મેળવો. - Vidyadip

MCQ

જો $f(x) = {\log _x}(\log x),$ તો $f'(x)$ એ $x = e$ આગળ મેળવો.

A
$e$
✓
${1 \over e}$
C
$1$
D
એક પણ નહીં

✓

Answer

Correct option: B.

${1 \over e}$

(b) $f(x) = {\log _x}(\log x) = \frac{{\log (\log x)}}{{\log x}}$

==> $f'(x) = \frac{{\frac{1}{x} - \frac{1}{x}\log (\log x)}}{{{{(\log x)}^2}}} \Rightarrow f'(e) = \frac{{\frac{1}{e} - 0}}{1} = \frac{1}{e}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 5. continuity and differentiation→5. continuity and differentiation — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

$\left| {\,\begin{array}{*{20}{c}}{265}&{240}&{219}\\{240}&{225}&{198}\\{219}&{198}&{181}\end{array}\,} \right|$ =

$\int \frac{d x}{x\left(x^{2}+1\right)}$ equals

$\int_{\,1}^{\,x} {\frac{{\log {x^2}}}{x}\,dx = } $

જો $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^{2}}=p$ તો $\tan p$ ની કિમંત મેળવો.

જો $A = \left[ {\begin{array}{*{20}{c}}4&{x + 2}\\{2x - 3}&{x + 1}\end{array}} \right]$ એ સંમિત શ્રેણિક હોય , તો $x =$

$\int_{}^{} {\frac{{{{\sin }^2}x - {{\cos }^2}x}}{{{{\sin }^2}x{{\cos }^2}x}}dx = } $

$\int_{1}^{5} (|x-3|+|x-1|)dx=\ ........$

જો વિધેય $f(x) = \left\{ \begin{array}{l}\frac{{{x^2} - 1}}{{x - 1}},\,\,{\rm{when}}\,\,x \ne 1\\\,\,\,\,\,\,\,\,\,\,\,\,k,\,{\rm{when}}\,\,x = 1\end{array} \right.$ એ $x = 1$ આગળ સતત હોય , તો $k$ મેળવો.

અનંત શ્રેણી ${\tan ^{ - 1}}\left( {\frac{2}{{1 - {1^2} + {1^4}}}} \right) + {\tan ^{ - 1}}\left( {\frac{4}{{1 - {2^2} + {2^4}}}} \right) + {\tan ^{ - 1}}\left( {\frac{6}{{1 - {3^2} + {3^4}}}} \right) + .....$ નો સરવાળો મેળવો.

જો $AA^T = I$ અને $C$ એ વિસંમિત શ્રેણિક છે તો $((A^T CA)^{50})^T$ મેળવો.