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The Chain Rule

AP Calculus AB· difficulty 3/5

H(x)=f(g(x))H(x) = f(g(x)) with g(1)=4g(1) = 4, g′(1)=−2g'(1) = -2, f′(4)=5f'(4) = 5. Then H′(1)=H'(1) =

  • A

    55

  • B

    1010

  • C

    −3-3

  • D

    −10-10

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Explanation

H′(1)=f′(g(1))⋅g′(1)=5⋅(−2)=−10H'(1) = f'(g(1)) \cdot g'(1) = 5 \cdot (-2) = -10.

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