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Applying the Power Rule

AP Calculus AB· difficulty 2/5

If f(x)=(x2−3)2f(x) = (x^2 - 3)^2, then f′(x)=f'(x) = (expand or use rule)

  • A

    2x2x

  • B

    2(x2−3)2(x^2 - 3)

  • C

    x4−6x2x^4 - 6x^2

  • D

    4x(x2−3)4x(x^2 - 3)

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Explanation

Chain rule: 2(x2−3)⋅(2x)=4x(x2−3)2(x^2-3) \cdot (2x) = 4x(x^2-3). (Also expand: x4−6x2+9x^4 - 6x^2 + 9, derivative 4x3−12x=4x(x2−3)4x^3 - 12x = 4x(x^2-3).)

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