Calculating Higher-Order Derivatives
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the second derivative of
f
(
x
)
=
x
2
+
2
x
+
1
f(x) = x^2 + 2x + 1
f
(
x
)
=
x
2
+
2
x
+
1
?
QUESTION
Calculate the second derivative of
f
(
x
)
=
1
4
x
4
+
x
f(x) = \frac{1}{4}x^4 + x
f
(
x
)
=
4
1
x
4
+
x
.
QUESTION
What is the second derivative of
f
(
x
)
=
x
3
f(x) = x^3
f
(
x
)
=
x
3
?
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ANSWER
f
′
′
(
x
)
=
6
x
f''(x) = 6x
f
′′
(
x
)
=
6
x
. Apply power rule twice:
f
′
(
x
)
=
3
x
2
f'(x) = 3x^2
f
′
(
x
)
=
3
x
2
, then
f
′
′
(
x
)
=
6
x
f''(x) = 6x
f
′′
(
x
)
=
6
x
.
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