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Mathematics
Mathematics
Problem
Find
d
d
x
(
x
2
sin
3
x
e
x
)
\dfrac{d}{dx}\left(\dfrac{x^{2}\sin 3x}{e^{x}}\right)
d
x
d
(
e
x
x
2
sin
3
x
)
. a)
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
+
x
2
sin
3
x
]
e^{-x}\bigl[2x\sin 3x + 3x^{2}\cos 3x + x^{2}\sin 3x\bigr]
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
+
x
2
sin
3
x
]
b)
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
−
x
2
sin
3
x
]
e^{-x}\bigl[2x\sin 3x + 3x^{2}\cos 3x - x^{2}\sin 3x\bigr]
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
−
x
2
sin
3
x
]
c)
e
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
−
x
2
sin
3
x
]
e^{x}\bigl[2x\sin 3x + 3x^{2}\cos 3x - x^{2}\sin 3x\bigr]
e
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
−
x
2
sin
3
x
]
d)
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
]
e^{-x}\bigl[2x\sin 3x + 3x^{2}\cos 3x\bigr]
e
−
x
[
2
x
sin
3
x
+
3
x
2
cos
3
x
]
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