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

What is the derivative of f(x)=5x+1x2−4f(x) = \frac{5x+1}{x^2-4}?

A.−5x2−2x−20(x2−4)2\frac{-5x^2 - 2x - 20}{(x^2-4)^2}
B.−5x2+2x−20(x2−4)2\frac{-5x^2 + 2x - 20}{(x^2-4)^2}
C.15x2+2x−20(x2−4)2\frac{15x^2 + 2x - 20}{(x^2-4)^2}
D.−5x2−2x−20x4−16\frac{-5x^2 - 2x - 20}{x^4 - 16}

Explanation

Core Concept

Applying the quotient rule gives 5(x2−4)−(5x+1)(2x)(x2−4)2\frac{5(x^2-4) - (5x+1)(2x)}{(x^2-4)^2}, which correctly expands and simplifies to this expression.

Correct Answer

A−5x2−2x−20(x2−4)2\frac{-5x^2 - 2x - 20}{(x^2-4)^2}

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