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Moderate

# Derivative Value of a Convergent Taylor Series

APCALC-1EXUNB

Given that $\sum _{ n=0 }^{ \infty }{ { a }_{ n } } { x }^{ n }$ is a Taylor series that converges to $f\left( x \right)$ for all real $x$, $f^{ ' }\left( 1 \right) =$

A

$0$

B

$\sum _{ n=0 }^{ \infty }{ { a }_{ n } }$

C

$\sum _{ n=0 }^{ \infty }{ { na }_{ n } }$

D

$\sum _{ n=0 }^{ \infty }{ { a }_{ n } } nx$