The chain rule of differentiation gives the derivative of f(g(x)) as f'(g(x))*g'(x)

For f(x) = (x^3 + 4)^4

we can take u(x) = x^3 + 4

f(x) = (u(x))^4

f'(x) = 4*(u(x))^3*u'(x)

=> f'(x) = 4*(x^3 + 4)^3 * 3x^2

=> f'(x) = 12x^2*(x^3 +4)^3

**The derivative of (x^3 + 4)^4 = 12x^2*(x^3 +4)^3**