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AP® Calculus AB-BC

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Moderate

Find the Nth Derivative of an Exponential Function

APCALC-QNLEOM

If $f(x)=e^{-3x+1}$, what does $f^{(n)} (x)$ equal?

A

$f^{(n)} (x) = -(3^n) \cdot e^{-3x+1} $

B

$f^{(n)} (x) = (-1)^n \cdot 3^n \cdot e^{-3x+1}$

C

$f^{(n)} (x)=(-1)^n \cdot 3e^{-3x+1}$

D

$f^{(n)} (x)=(-1)^{n+1} \cdot 3e^{-3x+1}$