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Let $f^{-1} (x)$ be the inverse of $f(x)=x^3+3x$. Find $\left( f^{-1} \right)'(4)$.

A

$\left( f^{-1} \right)'(4)=-6$

B

$\left( f^{-1} \right)'(4)=\cfrac{1}{6}$

C

$\left( f^{-1} \right)'(4)=-51$

D

$\left( f^{-1} \right)'(4)=\cfrac{1}{51}$

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