If \(f\left( x \right) =\begin{vmatrix} x^n & \sin x  & -\cos x  \\ n! & \...

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If \(f\left( x \right) =\begin{vmatrix} x^n & \sin x  & -\cos x  \\ n! & \sin \left(\displaystyle \frac{n\pi}{2} \right)  & \cos\left( \displaystyle \frac{n\pi}{2} \right)  \\ a & a^{ 2 } & a^{ 3 } \end{vmatrix}\) , then the value of \(\displaystyle \frac{d^{n}}{dx^{n}}\left ( f\left ( x \right ) \right )\) at \(x=0\) for \(n=2m+1\) is
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