If $f(x)=\left|\begin{array}{ccc}2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \ 3+2 \cos ^4 x & 2 \sin ^4 x & \sin ^2 2 x \ 2 \cos ^4 x & 3+2 \sin ^4 x & \sin ^2 2 x\end{array}\right|$, then $\frac{1}{5} f^{\prime}(0)$ is equal to : [JEE Main 2024, 30 Jan (Shift 1)]

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If \(f(x)=\left|\begin{array}{ccc}2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x &…

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If \(f(x)=\left|\begin{array}{ccc}2 \cos ^4 x &amp; 2 \sin ^4 x &amp; 3+\sin ^2 2 x \\ 3+2 \cos ^4 x &amp; 2 \sin ^4 x &…

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If \(f(x)=\left|\begin{array}{ccc}2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x &…