12th Class
Mathematics
Sample Paper
Maths Olympiad Model Paper-1
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: