F(x)= ln((3x+6)^4 (x^3 -2)^5 )
F'(x)=
I would first simplify that log expression
= log (3x+6)^4 + log (x^3-2)^5
= 4 log (3x+6) + 5 log (x^3 - 2)
now take the derivative
f ' (x) = 4(3/(3x+6) + 5(3x2)/(x^3 - 2)
= 4/(x+2) + 15x^2/(x^3 - 2)
add them up if needed.