Victor's complicated yet simple problem

Level pending

Let \(f(x)=(x^{2}+x+1)(x^{3}−x^{2}+1)\). What is the sum of the digits of the closest integer to \(f'(3.14)\)?

Details and Assumptions

For example, if \(f(x)=x^{2}, f'(x)=2x, f'(1)=2(1)=2\).

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