differentiate cot root 3
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Find the Derivative - d/dx f(x)=cot( square root of x)^3
f
(
x
)
=
cot
3
(
√
x
)
Rewrite
√
x
as
x
1
2
.
d
d
x
[
cot
3
(
x
1
2
)
]
Differentiate using the chain rule, which states that
d
d
x
[
f
(
g
(
x
)
)
]
is
f
'
(
g
(
x
)
)
g
'
(
x
)
where
f
(
x
)
=
x
3
and
g
(
x
)
=
cot
(
x
1
2
)
.
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3
cot
2
(
x
1
2
)
d
d
x
[
cot
(
x
1
2
)
]
Differentiate using the chain rule, which states that
d
d
x
[
f
(
g
(
x
)
)
]
is
f
'
(
g
(
x
)
)
g
'
(
x
)
where
f
(
x
)
=
cot
(
x
)
and
g
(
x
)
=
x
1
2
.
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3
cot
2
(
x
1
2
)
(
−
csc
2
(
x
1
2
)
d
d
x
[
x
1
2
]
)
Differentiate using the Power Rule.
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−
3
cot
2
(
x
1
2
)
csc
2
(
x
1
2
)
(
1
2
x
1
2
−
1
)
To write
−
−
1
1
as a fraction with a common denominator, multiply by
2
2
.
−
3
cot
2
(
x
1
2
)
csc
2
(
x
1
2
)
(
1
2
x
1
2
+
−
1
1
⋅
2
2
)
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