Consider $F(x)={\displaystyle \underset{1}{\overset{2x}{}}}\frac{1}{1+t^3}dt.$ Find $F^{\text{'}}(x).$

$(A)\frac{1}{1+8x^2}$

$(B)\frac{1}{1+2x^2}$

$(C)\frac{2}{1+8x^3}-\frac{1}{2}$

$(D)\frac{2}{1+8x^3}$

A reminder $to$ show ALL work that leads $to$ your answer.

$If$ a written explanation $in$ words $is$ necessary, please $be$

sure $to$ include $it.No$ Work, $No$ Credit!