Use part I of the Fundamental Theorem of Calculus to find the derivative of
\[
\begin{array}{l}
f(x)=\int_{3}^{x}\left(\frac{1}{3} t^{2}-1\right)^{7} d t \\
f^{\prime}(x)=
\end{array}
\]

Answer

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Answer

Therefore, the derivative of the function is \(\boxed{(\frac{1}{3x^2} - 1)^7}\)

Steps

Step 1 ：Given the function \(f(x) = \int_{3}^{x} (\frac{1}{3t^2} - 1)^7 dt\)

Step 2 ：According to the Fundamental Theorem of Calculus Part I, the derivative of this function is simply the integrand evaluated at x

Step 3 ：So, we have \(f'(x) = (\frac{1}{3x^2} - 1)^7\)

Step 4 ：Therefore, the derivative of the function is \(\boxed{(\frac{1}{3x^2} - 1)^7}\)