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EXAMPLE 7
Using the Power Rule for Functions to Find a Derivative
(a)
If
f
(
x
)
=
(
3
−
x
3
)
−
5
, then
f
′
(
x
)
=
d
d
x
(
3
−
x
3
)
−
5
=
↑
Power Rule
for Functions
−
5
(
3
−
x
3
)
−
5
−
1
⋅
d
d
x
(
3
−
x
3
)
=
−
5
(
3
−
x
3
)
−
6
⋅
(
−
3
x
2
)
=
15
x
2
(
3
−
x
3
)
−
6
=
15
x
2
(
3
−
x
3
)
6
(b)
If
f
(
θ
)
=
cos
3
θ
, then
f
(
θ
)
=
(
cos
θ
)
3
,
and
f
′
(
θ
)
=
d
d
θ
(
cos
θ
)
3
=
↑
Power Rule
for Functions
3
(
cos
θ
)
3
−
1
⋅
d
d
θ
cos
θ
=
3
cos
2
θ
⋅
(
−
sin
θ
)
=
−
3
cos
2
θ
sin
θ
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