Question

The value of $\frac{d}{dx}\left(lo{g}_{2}lo{g}_{3}x\right)$ at $x=3$ is

• A. $\frac{1}{\ell n2\ell n3}$
• B. $\frac{1}{\ell n8\ell n3}$
• C. $\frac{1}{\ell n4\ell n3}$
• D. $\frac{1}{\ell n2\ell n9}$

Answer 1

The correct option is B $\frac{1}{\ell n8\ell n3}$

$\frac{d}{dx}\left(lo{g}_{2}lo{g}_{3}x\right)\Rightarrow \frac{1}{ln2ln3}[\frac{1}{lo{g}_{3}x}.\frac{1}{x}]$

$\therefore$ at $x=3,$

$\Rightarrow \frac{1}{ln2ln3.1.3}=\frac{1}{3ln2ln3}=\frac{1}{lm8ln3}$