Let f(x)=∣cos⁡3xsin⁡xcos⁡xcos⁡2xsin⁡2x2cos⁡2xcos⁡3xsin⁡3x3cos⁡3x∣f(x) = \begin{vmatrix} \cos 3x & \sin x & \cos x \\ \cos 2x & \sin 2x & 2\cos 2x \\ \cos 3x & \sin 3x & 3\cos 3x \end{vmatrix}…

Mathematics

Problem

Let f(x)=∣cos⁡3xsin⁡xcos⁡xcos⁡2xsin⁡2x2cos⁡2xcos⁡3xsin⁡3x3cos⁡3x∣f(x) = \begin{vmatrix} \cos 3x & \sin x & \cos x \\ \cos 2x & \sin 2x & 2\cos 2x \\ \cos 3x & \sin 3x & 3\cos 3x \end{vmatrix} then find the value of f′(π2)f'\left(\frac{\pi}{2}\right) .

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