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Problems
Let
f
(
x
)
=
∣
x
3
sin
x
cos
x
6
−
1
0
p
p
2
p
3
∣
,
f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix},
f
(
x
)
=
x
3
6
p
sin
x
−
1
p
2
cos
x
0
p
3
,
…
Mathematics
Problem
Let
f
(
x
)
=
∣
x
3
sin
x
cos
x
6
−
1
0
p
p
2
p
3
∣
,
f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix},
f
(
x
)
=
x
3
6
p
sin
x
−
1
p
2
cos
x
0
p
3
,
where
p
p
p
is a constant. Then
d
3
d
x
3
{
f
(
x
)
}
\frac{d^3}{dx^3}\{f(x)\}
d
x
3
d
3
{
f
(
x
)}
at
x
=
0
x = 0
x
=
0
is a.
p
p
p
b.
p
+
p
2
p + p^2
p
+
p
2
c.
p
+
p
3
p + p^3
p
+
p
3
d. independent of
p
p
p
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