question_answer

Let \[f(x)=\left| \begin{matrix}    {{x}^{3}} & \sin x & \cos x  \\    6 & -1 & 0  \\    p & {{p}^{2}} & {{p}^{3}}  \\ \end{matrix} \right|,\] where p is constant. Then \[\frac{{{d}^{3}}}{d{{x}^{3}}}\,\,f\,\,(x)\] at \[x=0\]is:

A)  \[p\]                            

B)  \[p+{{p}^{2}}\]

C)  \[p+{{p}^{3}}\]                    

D)  independent of p

E)  None of these