The Chain Rule

AP Calculus AB· difficulty 3/5

Given g(2)=5g(2) = 5, g(2)=3g'(2) = 3, f(5)=7f'(5) = 7, find (fg)(2)(f \circ g)'(2).

  • A

    2121

    check_circle
  • B

    1010

  • C

    3535

  • D

    1515

Explanation

(fg)(2)=f(g(2))g(2)=f(5)g(2)=73=21(f \circ g)'(2) = f'(g(2)) \cdot g'(2) = f'(5) \cdot g'(2) = 7 \cdot 3 = 21.

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