Answer
$F'(1) = 198$
Work Step by Step
$F(x) = f(xf(xf(x)))$
$F'(x) = f'(xf(xf(x)))\cdot\frac{d}{dx}(xf(xf(x)))$
$F'(x) = f'(xf(xf(x)))\cdot~[f(xf(x))+x~f'(xf(x))*(xf(x))']$
$F'(x) = f'(xf(xf(x)))\cdot~[f(xf(x))+x~f'(xf(x))*(xf'(x)+1f(x))]$
$F'(1) = f'(1f(1f(1)))\cdot~[f(1f(1))+1~f'(1f(1))*(1*f'(1)+1*f(1))]$
$F'(1) = f'(f(f(1)))\cdot~[f(f(1))+f'(f(1))*(4+2)]$
$F'(1) = f'(f(2))\cdot~[f(2)+f'(2)*(4+2)]$
$F'(1) = f'(3)\cdot~[3+5*6]$
$F'(1) = (6)\cdot~(33)$
$F'(1) = 198$
