The rule for deriving composite functions (known as the chain rule) is:
[tex] (f(g(x))' = f'(g(x))\cdot g'(x) [/tex]
So, in your case, we have
[tex] F'(3) = f'(g(3))\cdot g'(3) [/tex]
We know that [tex] g'(3) = 4 [/tex] and [tex] g(3)=6[/tex]
So, the expression becomes
[tex] F'(3) = f'(6)\cdot 4 [/tex]
Finally, since [tex] f'(6)=8 [/tex], we have
[tex] F'(3) = 8\cdot 4 = 32[/tex]
