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Mathematics
Problem
Which expression gives the
n
n
n
th derivative of a function
f
f
f
at
x
=
a
x=a
x
=
a
in terms of the coefficient
c
n
c_n
c
n
of
(
x
−
a
)
n
(x-a)^n
(
x
−
a
)
n
in its Taylor polynomial centered at
x
=
a
x=a
x
=
a
? a)
(
n
−
1
)
!
c
n
(n-1)!\,c_n
(
n
−
1
)!
c
n
b)
c
n
n
!
\dfrac{c_n}{n!}
n
!
c
n
c)
n
!
c
n
n!\,c_n
n
!
c
n
d)
c
n
c_n
c
n
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