find dy÷dx if y =e^-3x cos x
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Given
f
(
x
)
=
e
3
x
⋅
cos
(
2
x
)
Use the formula
d
d
x
(
u
v
)
=
u
⋅
d
d
x
(
v
)
+
v
⋅
d
d
x
(
u
)
Let
u
=
e
3
x
and
v
=
cos
(
2
x
)
d
d
x
(
u
v
)
=
u
⋅
d
d
x
(
v
)
+
v
⋅
d
d
x
(
u
)
f
'
(
x
)
=
d
d
x
(
e
3
x
⋅
cos
(
2
x
)
)
=
e
3
x
⋅
d
d
x
(
cos
(
2
x
)
)
+
cos
(
2
x
)
⋅
d
d
x
(
e
3
x
)
f
'
(
x
)
=
e
3
x
⋅
−
sin
(
2
x
)
⋅
d
d
x
(
2
x
)
+
cos
(
2
x
)
⋅
e
3
x
⋅
d
d
x
(
3
x
)
f
'
(
x
)
=
e
3
x
⋅
(
−
sin
(
2
x
)
)
(
2
)
+
cos
(
2
x
)
e
3
x
(
3
)
simplify by factoring common factors
f
'
(
x
)
=
e
3
x
⋅
[
3
⋅
cos
2
x
−
2
⋅
sin
2
x
]
God bless...I hope the explanation is usefu
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