a little confused on this derivative, my professor posted the answers and he has this answer as $\displaystyle \frac{-19}{112}$ but i'm not seeing how he's getting that. any help is really appreciated.

find the derivative and $\displaystyle f\prime(2)$

$\displaystyle f(x) = \frac{x^3+2x+3}{x^4+3x+6}

$

if i use product rule i get

$\displaystyle

f\prime(x) = \frac{(3x^2+2)(x^4+3x+6) - (x^3+2x+3)(4x^3+3)}{(x^4+3x+6)^2}$

i've done it two different ways and come up with $\displaystyle \frac{-35}{784} or \frac{-133}{784}$

please help, final is tomorrow !