Use logarithmic differentiation:
F(x)= (3x+6)^4 (x^3 -2)^5
f'(x)=
ln f = 4ln(3x+6) + 5ln(x^3-2)
1/f f' = 12/(3x+6) + 15x^2/(x^3-2)
now multiply by f and simplify fractions
F(x)= (3x+6)^4 (x^3 -2)^5
f'(x)=
1/f f' = 12/(3x+6) + 15x^2/(x^3-2)
now multiply by f and simplify fractions