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Mathematics
Mathematics
Problem
For
f
(
x
)
=
ln
(
3
x
)
sin
(
2
x
)
e
x
f(x)=\ln(3x)\,\sin(2x)\,e^{x}
f
(
x
)
=
ln
(
3
x
)
sin
(
2
x
)
e
x
, which of the following equals
f
′
(
x
)
f'(x)
f
′
(
x
)
? a)
e
x
[
sin
(
2
x
)
x
+
2
ln
(
3
x
)
cos
(
2
x
)
]
e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\ln(3x)\cos(2x) \right]
e
x
[
x
sin
(
2
x
)
+
2
ln
(
3
x
)
cos
(
2
x
)
]
b)
e
x
[
sin
(
2
x
)
x
+
2
ln
(
3
x
)
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\ln(3x)\cos(2x) + \ln(3x)\sin(2x) \right]
e
x
[
x
sin
(
2
x
)
+
2
ln
(
3
x
)
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
c)
e
x
[
sin
(
2
x
)
x
+
2
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
e^{x}\left[ \dfrac{\sin(2x)}{x} + 2\cos(2x) + \ln(3x)\sin(2x) \right]
e
x
[
x
sin
(
2
x
)
+
2
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
d)
e
x
[
sin
(
2
x
)
x
+
ln
(
3
x
)
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
e^{x}\left[ \dfrac{\sin(2x)}{x} + \ln(3x)\cos(2x) + \ln(3x)\sin(2x) \right]
e
x
[
x
sin
(
2
x
)
+
ln
(
3
x
)
cos
(
2
x
)
+
ln
(
3
x
)
sin
(
2
x
)
]
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