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Mathematics
Problem
d
d
x
[
e
a
x
sin
(
b
x
+
c
)
]
=
\frac{d}{dx} \left[ \frac{e^{ax}}{\sin(bx + c)} \right] =
d
x
d
[
s
i
n
(
b
x
+
c
)
e
a
x
]
=
(a)
e
a
x
[
a
sin
(
b
x
+
c
)
+
b
cos
(
b
x
+
c
)
]
sin
2
(
b
x
+
c
)
\frac{e^{ax}[a \sin(bx + c) + b \cos(bx + c)]}{\sin^2(bx + c)}
s
i
n
2
(
b
x
+
c
)
e
a
x
[
a
s
i
n
(
b
x
+
c
)
+
b
c
o
s
(
b
x
+
c
)]
(b)
e
a
x
[
a
sin
(
b
x
+
c
)
−
b
cos
(
b
x
+
c
)
]
sin
(
b
x
+
c
)
\frac{e^{ax}[a \sin(bx + c) - b \cos(bx + c)]}{\sin(bx + c)}
s
i
n
(
b
x
+
c
)
e
a
x
[
a
s
i
n
(
b
x
+
c
)
−
b
c
o
s
(
b
x
+
c
)]
(c)
e
a
x
[
a
sin
(
b
x
+
c
)
−
b
cos
(
b
x
+
c
)
]
sin
2
(
b
x
+
c
)
\frac{e^{ax}[a \sin(bx + c) - b \cos(bx + c)]}{\sin^2(bx + c)}
s
i
n
2
(
b
x
+
c
)
e
a
x
[
a
s
i
n
(
b
x
+
c
)
−
b
c
o
s
(
b
x
+
c
)]
(d) None of these
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