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Procedures for Calculating Derivatives

AP Calculus AB· difficulty 3/5

If f(x)=(x2+1)(x−3)f(x) = (x^2 + 1)(x - 3), then f′(x)=f'(x) =

  • A

    x2+1+(x−3)(2x)x^2 + 1 + (x - 3)(2x)

  • B

    2x+12x + 1

  • C

    2x(x−3)2x(x-3)

  • D

    3x2−6x+13x^2 - 6x + 1

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Explanation

Use product rule: 2x(x−3)+(x2+1)(1)=2x2−6x+x2+1=3x2−6x+12x(x-3) + (x^2+1)(1) = 2x^2 - 6x + x^2 + 1 = 3x^2 - 6x + 1.

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