AP Calculus ABmediummcq1 pt

If f(x)=exx2f(x)=\dfrac{e^x}{x^2}, then f(x)=f'(x)=

A.ex(x+2)x3\dfrac{e^x(x+2)}{x^3}
B.ex(x2)x3\dfrac{e^x(x-2)}{x^3}
C.ex2x\dfrac{e^x}{2x}
D.ex(x2)x4\dfrac{e^x(x-2)}{x^4}

Explanation

Core Concept

The quotient rule gives exx2ex(2x)x4\dfrac{e^x x^2-e^x(2x)}{x^4}. Canceling one factor of xx gives ex(x2)x3\dfrac{e^x(x-2)}{x^3}.

Correct Answer

Bex(x2)x3\dfrac{e^x(x-2)}{x^3}

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