Let \(f(x) = \left| {\begin{array}{*{20}{c}} {{x^3}}&{\sin x}&{\cos x}\\ 6&{ - 1}&0\\ p&{{p^2}}&{{p^3}} \end{array}} \right|\), where p is a constant, then \(\frac{{{d^3}}}{{d{x^3}}}\left( {f(x)} \right)\) at x = 0 is

Let \(f(x) = \left| {\begin{array}{*{20}{c}} {{x^3}}&{\sin x}&{\cos x

1.	Let \(f(x) = \left\| {\begin{array}{*{20}{c}} {{x^3}}&{\sin x}&{\cos x}\\ 6&{ - 1}&0\\ p&{{p^2}}&{{p^3}} \end{array}} \right\|\), where p is a constant, then \(\frac{{{d^3}}}{{d{x^3}}}\left( {f(x)} \right)\) at x = 0 is
A.	p
B.	p + p2
C.	p + p3
D.	independent of p
Answer» E.

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Let \(f(x) = \left| {\begin{array}{*{20}{c}} {{x^3}}&{\sin x}&{\cos x}\\ 6&{ - 1}&0\\ p&{{p^2}}&{{p^3}} \end{array}} \right|\), where p is a constant, then \(\frac{{{d^3}}}{{d{x^3}}}\left( {f(x)} \right)\) at x = 0 is

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