If [f(x)=|[arrayccc 2 ^4 x & 2 ^4 x & 3+ ^2 2 x 3+2 ^4 x & 2 ^4 x & ^2 2 x 2 ^4 x & 3+2 ^4…

Question

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 :

Accepted Answer

$$\begin{aligned}
& \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 ^2 4 x & \sin ^2 2 x \end{array}\end{aligned}$$\right| \
\& \mathrm{R}\_2 \rightarrow \mathrm{R}\_2-\mathrm{R}\_1, \mathrm{R}\_3 \rightarrow \mathrm{R}\_3-\mathrm{R}\_1 \
\& \left|$$\begin{array}{ccc} 2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \ 3 & 0 & -3 \ 0 & 3 & -3 \end{array}$$\right| \
\& \mathrm{f}(\mathrm{x})=45 \
\& \mathrm{f}\^{\prime}(\mathrm{x})=0 \
\&
\]

Solutions · 1