If f(x)=vmatrix 2 ^4x 2 ^4x 3+ ^22x 3+2 ^4x 2 ^4x ^22x 2 ^4x 3+2 ^4x ^22x vmatrix, then (1…

Question

If $f(x)=\begin{vmatrix} 2{\cos }^{4}x \quad  2{\sin }^{4}x \quad  3+{\sin }^{2}2x \ 3+2{\cos }^{4}x \quad  2{\sin }^{4}x \quad  {\sin }^{2}2x \ 2{\cos }^{4}x \quad  3+2{\sin }^{4}x \quad  {\sin }^{2}2x \end{vmatrix},$ then $\frac{1}{5}{f}^{'}(0)=$ is equal to :

Accepted Answer

$\begin{gathered} |\begin{array}{ccc}2{\cos }^{4}x \quad  2{\sin }^{4}x \quad  3+{\sin }^{2}2x \ 3+2{\cos }^{4}x \quad  2{\sin }^{4}x \quad  {\sin }^{2}2x \ 2{\cos }^{4}x \quad  3+2{\sin }^{2}4x \quad  {\sin }^{2}2x\end{array}| \ {R}_{2}	o {R}_{2}-{R}_{1},{R}_{3}	o {R}_{3}-{R}_{1} \ |\begin{array}{ccc}2{\cos }^{4}x \quad  2{\sin }^{4}x \quad  3+{\sin }^{2}2x \ 3 \quad  0 \quad  -3 \ 0 \quad  3 \quad  -3\end{array}| \ f(x)=45 \ {f}^{'}(x)=0 \end{gathered}$

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