Your answer is correct! The only thing you can do is put a factor outside in the numerator.
use the quotient rule to differentiate the function
I have got as far as
k '(x) =(x^3+8)(6e^6x)-(e^6x)(3x^2)/(x^3+8)^2
But im unsure how to take it any further would anyone be able to help us?
You just factor using simple algebra.
You can also find differentiation of in the following link:
differentiate (e^(6x))/(x^3+8) - Wolfram|Alpha