Differentiation of √3•sinx-cosx
Answers
Step-by-step explanation:
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Algebra Examples
Popular Problems Algebra Find the Derivative - d/dx 3sin(x)cos(x)
3
sin
(
x
)
cos
(
x
)
Since
3
is constant with respect to
x
, the derivative of
3
sin
(
x
)
cos
(
x
)
with respect to
x
is
3
d
d
x
[
sin
(
x
)
cos
(
x
)
]
.
3
d
d
x
[
sin
(
x
)
cos
(
x
)
]
Differentiate using the Product Rule which states that
d
d
x
[
f
(
x
)
g
(
x
)
]
is
f
(
x
)
d
d
x
[
g
(
x
)
]
+
g
(
x
)
d
d
x
[
f
(
x
)
]
where
f
(
x
)
=
sin
(
x
)
and
g
(
x
)
=
cos
(
x
)
.
3
(
sin
(
x
)
d
d
x
[
cos
(
x
)
]
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
The derivative of
cos
(
x
)
with respect to
x
is
−
sin
(
x
)
.
3
(
sin
(
x
)
(
−
sin
(
x
)
)
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
Raise
sin
(
x
)
to the power of
1
.
3
(
−
(
sin
1
(
x
)
sin
(
x
)
)
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
Raise
sin
(
x
)
to the power of
1
.
3
(
−
(
sin
1
(
x
)
sin
1
(
x
)
)
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
3
(
−
sin
(
x
)
1
+
1
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
Add
1
and
1
.
3
(
−
sin
2
(
x
)
+
cos
(
x
)
d
d
x
[
sin
(
x
)
]
)
The derivative of
sin
(
x
)
with respect to
x
is
cos
(
x
)
.
3
(
−
sin
2
(
x
)
+
cos
(
x
)
cos
(
x
)
)
Raise
cos
(
x
)
to the power of
1
.
3
(
−
sin
2
(
x
)
+
cos
1
(
x
)
cos
(
x
)
)
Raise
cos
(
x
)
to the power of
1
.
3
(
−
sin
2
(
x
)
+
cos
1
(
x
)
cos
1
(
x
)
)
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
3
(
−
sin
2
(
x
)
+
cos
(
x
)
1
+
1
)
Add
1
and
1
.
3
(
−
sin
2
(
x
)
+
cos
2
(
x
)
)