$\displaystyle y = \dfrac{x + 3}{x^{3} + x - 5}$

$\displaystyle \dfrac{dy}{dx} = \dfrac{[x^{3} + x - 5][\dfrac{d}{dx}(x + 3)] - [x + 3][\dfrac{d}{dx}(x^{3} + x - 5)]}{(x^{3} + x - 5)^{2}}$

$\displaystyle \dfrac{dy}{dx} = \dfrac{[x^{3} + x - 5][1] - [x + 3][3x + 1]}{(x^{3} + x - 5)^{2}}$