Calculating Higher-Order Derivatives
AP Calculus AB · Flashcards · Recall
AP CALCULUS AB · FLASHCARDS
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QUESTION
State the formula for the
n
n
n
-th derivative of
f
(
x
)
=
x
n
f(x) = x^n
f
(
x
)
=
x
n
.
QUESTION
State the formula for the
n
n
n
-th derivative of
f
(
x
)
=
x
n
f(x) = x^n
f
(
x
)
=
x
n
.
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ANSWER
f
(
n
)
(
x
)
=
n
!
f^{(n)}(x) = n!
f
(
n
)
(
x
)
=
n
!
if
n
n
n
is a positive integer. Each differentiation reduces the power by 1 and multiplies by the current power.
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