Find f$\text{'}($a$)$f$($a$).$

$$f$($t$)=2$t$+4$t$+4$f$($t$)=2$t$+4$t$+4$

$$

To find f$\text{'}($a$)$f$($a$),$ we will use the formula

f$\text{'}($a$)=$limt$$af$($t$)$f$($a$)$t$$af$($a$)=$limt$$af$($t$)-$f$($a$)$t$-$a$.$

Since f$($t$)=2$t$+4$t$+4$f$($t$)=2$t$+4$t$+4$ we have

$$f$\text{'}($a$)=$limt$$a$2$t$+4$t$+42$a$+4$a$+4$t$$af$($a$)=$limt$$a$2$t$+4$t$+4-2$a$+4$a$+4$t$-$a $.$

Simplifying everything we get

f$\text{'}($a$)=$limt$$af$($a$)=$limt$$a $6($t$$a$)($t$$a$)$