We can use the substitutions:

u = 4x² and v = x³ + 3

Using the quotient rule, we first need:

`(du)/(dx)=8x` and `(dv)/(dx)=3x^2`

Then

` {: ((d(u/v))/(dx),=(v(du)/(dx)-u(dv)/(dx))/v^2),(,=((x^3+3)(8x)-(4x^2)(3x^2))/((x^3+3)^2)),(,=(8x^4+24x-12x^4)/((x^3+3)^2)),(,=(-4x^4+24x)/((x^3+3)^2)) :}`