Hello, please consider the following.
f is differentiable so g is differentiable and we we can compute the derivative of g.
[tex]\text{derivative of } u^2\text{ is } 2uu'\\\\\text{derivative of } f(f(x^3)+x)\text{ is } (3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{So, }\\\\g'(x)=2f(f(x^3)+x)(3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{ We replace x par 1}\\\\g'(1)=2f(f(1)+1)(3f'(1)+1)f'(f(1)+1)\\\\g'(1)=2f(2)(3f'(1)+1)f'(2)\\\\\text{ We can put f'(2) in one part of the equation}\\\\f'(2)=\dfrac{2f(2)(3f'(1)+1)}{g'(1)}=\dfrac{2*5*(3*(-3)+1)}{2}\\\\=5*(-9+1)\\\\=5*(-8)\\\\=\boxed{-40}[/tex]
Thank you.
