?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Moderate

Comparing Exponential Derivative Notations for Equivalence

APCALC-WLXYUZ

Which of the following is NOT true if $y=f(x)=\frac{x^3}{e^x}$?

A

$f'(x)=\cfrac{3x^2e^x-x^3e^x}{e^{2x}}$

B

$y'=\cfrac{3x^2-x^3}{e^x}$

C

$\cfrac{dy}{dx}=-e^{-x} \cdot (x^3-3x^2)$

D

$\cfrac{d}{dx} (f(x))=\frac{3x^2}{e^x}$