Question

If $f\left(x\right)={\log }_5{\log }_{3}x$ then $f^{\prime }\left(e\right)$ is equal to

• A. $\frac{1}{e\log 3\log 5}$
• B. $\frac{e}{e\log 3\log 5}$
• C. $\frac{1}{e\log 5}$
• D. $\frac{1}{e\log 3}$

Answer 1

The correct option is A $\frac{1}{e\log 3\log 5}$

Given,

$f\left(x\right)=lo{g}_{5}lo{g}_{3}x$

$f\left(x\right)=\frac{log\left(lo{g}_{3}x\right)}{log5}$

Differentiate with respect to x-

$f^{\prime }\left(x\right)=\frac{1}{xlog3log5}$

$⟹f^{\prime }\left(e\right)=\frac{1}{elog3log5}$