Question $5(1$ point$)$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x).$

$f(x)=\sqrt[\phantom{2}]{9+x}{f}^{\text{'}}(x).\frac{1}{2\sqrt[\phantom{2}]{9+x}}$

$(II)\frac{1}{\sqrt[\phantom{2}]{9+x+h}+\sqrt[\phantom{2}]{9+x}}$

$(III)\frac{1}{\sqrt[\phantom{2}]{9+x+h}-\sqrt[\phantom{2}]{9+x}}$

$(IV)\frac{9}{\sqrt[\phantom{2}]{9+x+h}-\sqrt[\phantom{2}]{9+x}}$

$(V)\frac{9}{\sqrt[\phantom{2}]{9+x+h}+\sqrt[\phantom{2}]{9+x}}$

Choose the correct answer from the following. Note that the order $of$ answers below

has been randomized. $Be$ sure $to$ choose the correct Roman numeral corresponding

$to$ your choice.