# Is it possible to find the derivative of 3x/(x^2+4) without using the quotient rule?

$y = 3 x {\left({x}^{2} + 4\right)}^{-} 1$ so that you could use the Product and Chain Rule:
$y ' = 3 {\left({x}^{2} + 4\right)}^{-} 1 - 3 x {\left({x}^{2} + 4\right)}^{-} 2 \left(2 x\right) =$
$= 3 {\left({x}^{2} + 4\right)}^{-} 1 \left[1 - 2 {x}^{2} {\left({x}^{2} + 4\right)}^{-} 1\right] =$
$= \frac{3}{{x}^{2} + 4} \left[1 - 2 {x}^{2} / \left({x}^{2} + 4\right)\right] =$
$= \frac{3}{{x}^{2} + 4} ^ 2 \left[{x}^{2} + 4 - 2 {x}^{2}\right] =$
$= \frac{3}{{x}^{2} + 4} ^ 2 \left[4 - {x}^{2}\right]$