Use chain rule of differentiation and find derivative of f(x)=(x^3+4)^4?

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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

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