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Mathematics
Problem
Let
f
(
x
)
=
x
arcsec
(
3
x
)
f(x)=x\,\operatorname{arcsec}(3x)
f
(
x
)
=
x
arcsec
(
3
x
)
for
x
>
1
3
x>\frac{1}{3}
x
>
3
1
. Which of the following is
f
′
(
x
)
f'(x)
f
′
(
x
)
? a)
arcsec
(
3
x
)
+
1
x
9
x
2
−
1
\operatorname{arcsec}(3x)+\frac{1}{x\sqrt{9x^{2}-1}}
arcsec
(
3
x
)
+
x
9
x
2
−
1
1
b)
arcsec
(
3
x
)
+
3
x
9
x
2
−
1
\operatorname{arcsec}(3x)+\frac{3x}{\sqrt{9x^{2}-1}}
arcsec
(
3
x
)
+
9
x
2
−
1
3
x
c)
arcsec
(
3
x
)
+
1
9
x
2
−
1
\operatorname{arcsec}(3x)+\frac{1}{\sqrt{9x^{2}-1}}
arcsec
(
3
x
)
+
9
x
2
−
1
1
d)
1
+
1
9
x
2
−
1
1+\frac{1}{\sqrt{9x^{2}-1}}
1
+
9
x
2
−
1
1
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