Question

Let f(x) = loge $\left\{\frac{u\left(x\right)}{v\left(x\right)}\right\}$, u’(2) = 4, v’(2) = 2, u(2) = 2, v(2) = 1, then f’(2) is equal to

• A. 1
• B. -1
• C. none of these

Answer 1

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