Question

Let $f\left(x\right)=lo{g}_e\left\{\frac{u\left(x\right)}{v\left(x\right)}\right\},u^{\prime }\left(2\right)=4,v^{\prime }\left(2\right)=2,u\left(2\right)=2,v\left(2\right)=1$, then $f^{\prime }\left(2\right)$ is equal to

• A. 0.0
• B. 1
• C. - 1
• D. None of these

Answer 1

The correct option is A 0

$f\left(x\right)=lo{g}_e\left\{\frac{u\left(x\right)}{v\left(x\right)}\right\}$
$=lo{g}_{e}u\left(x\right)-lo{g}_{e}v\left(x\right)$
$\therefore f^{\prime }\left(x\right)=\frac{u^{\prime }\left(x\right)}{u\left(x\right)}-\frac{v^{\prime }\left(x\right)}{v\left(x\right)}$
$f^{\prime }\left(2\right)=\frac{u^{\prime }\left(2\right)}{u\left(2\right)}-\frac{v^{\prime }\left(2\right)}{v\left(2\right)}$
$=\frac{4}{2}-\frac{2}{1}$
$=2-2=0$