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Let \( f(x)=\exp \left(x^{3}+x^{2}+x\right) \) for any real number \( x \)
\( \mathrm{P} \) and let \( g \) be the inverse function for \( f \). The value of

W \( g^{\prime}\left(e^{3}\right) \) is
(A) \( \frac{1}{6 e^{3}} \)
(B) \( \frac{1}{6} \)
(C) \( \frac{1}{34 e^{39}} \)
(D) 6
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