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The Quotient Rule

AP Calculus AB· difficulty 4/5

ddxsin⁡xx\dfrac{d}{dx}\dfrac{\sin x}{x} at x=π/2x = \pi/2 is

  • A

    00

  • B

    −4π2-\frac{4}{\pi^2}

    check_circle
  • C

    11

  • D

    2π\frac{2}{\pi}

Explanation

Quotient: (xcos⁡x−sin⁡x)/x2(x\cos x - \sin x)/x^2. At x=π/2x=\pi/2: (π/2⋅0−1)/(π2/4)=−1/(π2/4)=−4/π2(\pi/2 \cdot 0 - 1)/(\pi^2/4) = -1/(\pi^2/4) = -4/\pi^2.

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