# Thread: derivative help

1. ## derivative help

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

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

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

if i use product rule i get

$

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 $\frac{-35}{784} or \frac{-133}{784}$

Your derivative is correct and $f'(2)=\frac{-133}{784}$