Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABeasymcq1 pt

If f(x)=x−1x+1f(x)=\dfrac{x-1}{x+1}, then f′(x)=f'(x)=

A.−2(x+1)2-\dfrac{2}{(x+1)^2}
B.2(x+1)2\dfrac{2}{(x+1)^2}
C.2(x−1)2\dfrac{2}{(x-1)^2}
D.11

Explanation

Core Concept

The quotient rule gives 1⋅(x+1)−(x−1)⋅1(x+1)2=2(x+1)2\dfrac{1\cdot(x+1)-(x-1)\cdot1}{(x+1)^2}=\dfrac{2}{(x+1)^2}. The numerator simplifies to x+1−x+1=2x+1-x+1=2.

Correct Answer

B2(x+1)2\dfrac{2}{(x+1)^2}

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