Differentiation of (3x-4)^3/2
Answers
Explanation:
Expand
(
3
x
−
4
)
(
3
x
−
4
)
using the FOIL Method.
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d
d
x
[
3
x
(
3
x
)
+
3
x
⋅
−
4
−
4
(
3
x
)
−
4
⋅
−
4
]
Simplify and combine like terms.
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d
d
x
[
9
x
2
−
24
x
+
16
]
By the Sum Rule, the derivative of
9
x
2
−
24
x
+
16
with respect to
x
is
d
d
x
[
9
x
2
]
+
d
d
x
[
−
24
x
]
+
d
d
x
[
16
]
.
d
d
x
[
9
x
2
]
+
d
d
x
[
−
24
x
]
+
d
d
x
[
16
]
Since
9
is constant with respect to
x
, the derivative of
9
x
2
with respect to
x
is
9
d
d
x
[
x
2
]
.
9
d
d
x
[
x
2
]
+
d
d
x
[
−
24
x
]
+
d
d
x
[
16
]
Differentiate using the Power Rule which states that
d
d
x
[
x
n
]
is
n
x
n
−
1
where
n
=
2
.
9
(
2
x
)
+
d
d
x
[
−
24
x
]
+
d
d
x
[
16
]
Multiply
2
by
9
.
18
x
+
d
d
x
[
−
24
x
]
+
d
d
x
[
16
]
Since
−
24
is constant with respect to
x
, the derivative of
−
24
x
with respect to
x
is
−
24
d
d
x
[
x
]
.
18
x
−
24
d
d
x
[
x
]
+
d
d
x
[
16
]
Differentiate using the Power Rule which states that
d
d
x
[
x
n
]
is
n
x
n
−
1
where
n
=
1
.
18
x
−
24
⋅
1
+
d
d
x
[
16
]
Multiply
−
24
by
1
.
18
x
−
24
+
d
d
x
[
16
]
Since
16
is constant with respect to
x
, the derivative of
16
with respect to
x
is
0
.
18
x
−
24
+
0
Add
18
x
−
24
and
0
.
18
x
−
24