If ,(x) = _5 , _3 ,x; then ' ,(e) is equal to - Vidyadip

MCQ

If $\phi \,(x) = {\log _5}\,{\log _3}\,x;$ then $\phi '\,(e)$ is equal to

A
$ e\ log\ 5$
B
$- e\ log\ 5$
✓
$\frac{1}{{e\,\ln \,5}}$
D
$\frac{log 5}{{e}}$

✓

Answer

Correct option: C.

$\frac{1}{{e\,\ln \,5}}$

c
$\phi(\mathrm{x})=\log _{5} \log _{3} \mathrm{x}$

$\phi(\mathrm{x})=\log _{\mathrm{s}}\left(\frac{\ln \mathrm{x}}{\ln 3}\right)$

$\phi ({\rm{x}}) = {\log _{\rm{s}}}{\rm{lnx}} - {\log _{\rm{s}}}\ln 3$

$\phi(x)=\frac{\ln \ln x}{\ln 5}-\log _{5} \ln 3$

$\phi^{\prime}(x)=\frac{1}{\ln 5} \times \frac{1}{\ln x} \times \frac{1}{x}$

${\phi ^\prime }(e) = \frac{1}{{e\ln S}}$

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