The function in the general form:
y=ln(f(x))
then its derivative is
y'=1/f(x)*f'(x)
where f(x)=(color(red)g(x))^5
and its derivative is:
f'(x)=5(color(red)g(x))^4*g'(x)
where color(red)(g(x)=-(4x^4)/(x^3-3))
and its derivative is:
g'(x)=((-4*4x^3)(x^3-3)-(-4x^4)(3x^2))/(x^3-3)^2
=(-16x^6+48x^3+12x^6)/(x^3-3)^2
=(48x^3-4x^6)/(x^3-3)^2=(4x^3(12-x^3))/(x^3-3)^2
Finally, it is:
y'=1/(color(red)g(x))^5*5(color(red)g(x))^4*g'(x)
=1/(-(4x^4)/(x^3-3))^cancel5*5cancel((-(4x^4)/(x^3-3))^4)*(4x^3(12-x^3))/(x^3-3)^2
=-(5cancel((x^3-3)))/(cancel4x^cancel4)*(cancel(4x^3)(12-x^3))/(x^3-3)^cancel2
=-(5(12-x^3))/(x(x^3-3))