AP Calculus ABeasymcq1 pt

If f(x)=x3f(x)=x^{-3}, then f(x)=f'(x)=

A.3x2-3x^{-2}
B.3x43x^{-4}
C.x4-x^{-4}
D.3x4-3x^{-4}

Explanation

Core Concept

The power rule applies to negative exponents: ddx[x3]=3x4\dfrac{d}{dx}[x^{-3}]=-3x^{-4}. Multiply by the exponent 3-3 and decrease the exponent by one.

Correct Answer

D3x4-3x^{-4}

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