`" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}|` then find the values of f(0) and f'`(pi//2)`.

Explanation

To solve the problem, we need to find the values of \( f(0) \) and \( f'(\frac{\pi}{2}) \) for the determinant defined as:

\[
f(x) = \begin{vmatrix}
\cos x & \sin x & \cos x \\
\cos 2x & \sin 2x & 2 \cos 2x \\
\cos 3x & \sin 3x & 3 \cos 3x
\end{vmatrix}
...