Question

State true or false:

If $u\left(x\right)$ and $v\left(x\right)$ are differentiable functions such that $\frac{u}{v}\left(x\right)=7$ If $\frac{u^{\prime }\left(x\right)}{v^{\prime }\left(x\right)}=p$ and ${\left(\frac{u\left(x\right)}{v\left(x\right)}\right)}^{\prime }=q$, then $\frac{p+q}{p-q}=1$.

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{u\left(x\right)}{v\left(x\right)}=7\Rightarrow u\left(x\right)=7v\left(x\right)\Rightarrow u^{\prime }\left(x\right)=7v^{\prime }\left(x\right)$
$\therefore \frac{u^{\prime }\left(x\right)}{v^{\prime }\left(x\right)}=7=p$ & $q=0$
so $\frac{p+q}{p-q}=1$