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Calculating Higher-Order Derivatives

AP Calculus AB· difficulty 3/5

For f(x)=sin⁡xf(x) = \sin x, the 100th derivative f(100)(x)f^{(100)}(x) equals

  • A

    cos⁡x\cos x

  • B

    −sin⁡x-\sin x

  • C

    −cos⁡x-\cos x

  • D

    sin⁡x\sin x

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Explanation

Derivatives cycle every 4: sin⁡,cos⁡,−sin⁡,−cos⁡\sin, \cos, -\sin, -\cos. 100≡0(mod4)100 \equiv 0 \pmod 4, so back to sin⁡x\sin x.

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