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National
Medium
Calculus
10–12
If
f
(
x
)
=
(
3
x
2
−
1
)
4
f(x) = (3x^{2} - 1)^{4}
f
(
x
)
=
(
3
x
2
−
1
)
4
, what is
f
′
(
1
)
f'(1)
f
′
(
1
)
?
Sendo
f
(
x
)
=
(
3
x
2
−
1
)
4
f(x) = (3x^{2} - 1)^{4}
f
(
x
)
=
(
3
x
2
−
1
)
4
, qual é
f
′
(
1
)
f'(1)
f
′
(
1
)
?
Answer options
A.
96
96
96
B.
192
192
192
C.
32
32
32
D.
384
384
384
Check Answer
Solution
Step 1 of 3
1.
By the chain rule,
f
′
(
x
)
=
4
(
3
x
2
−
1
)
3
×
6
x
f'(x) = 4(3x^{2} - 1)^{3} \times 6x
f
′
(
x
)
=
4
(
3
x
2
−
1
)
3
×
6
x
.
Next step
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