AP Calculus ABeasymcq1 pt

If f(x)=xexf(x)=\dfrac{x}{e^x}, then f(x)=f'(x)=

A.x1ex\dfrac{x-1}{e^x}
B.1ex\dfrac{1}{e^x}
C.1xex\dfrac{1-x}{e^x}
D.1xe2x\dfrac{1-x}{e^{2x}}

Explanation

Core Concept

The quotient rule gives 1exxexe2x=1xex\dfrac{1\cdot e^x-x\cdot e^x}{e^{2x}}=\dfrac{1-x}{e^x}. One factor of exe^x cancels.

Correct Answer

C1xex\dfrac{1-x}{e^x}

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