The Chain Rule

AP Calculus AB· difficulty 3/5

ddxsin(x2)=\dfrac{d}{dx}\sqrt{\sin(x^2)} =

  • A

    2xcos(x2)\dfrac{2x}{\cos(x^2)}

  • B

    sin(x2)2x\dfrac{\sin(x^2)}{2x}

  • C

    xcos(x2)sin(x2)\dfrac{x \cos(x^2)}{\sqrt{\sin(x^2)}}

    check_circle
  • D

    cos(x2)2sin(x2)\dfrac{\cos(x^2)}{2\sqrt{\sin(x^2)}}

Explanation

Outer: 12sin(x2)\dfrac{1}{2\sqrt{\sin(x^2)}}. Middle: cos(x2)\cos(x^2). Inner: 2x2x. Product: 2xcos(x2)2sin(x2)=xcos(x2)sin(x2)\dfrac{2x\cos(x^2)}{2\sqrt{\sin(x^2)}} = \dfrac{x\cos(x^2)}{\sqrt{\sin(x^2)}}.

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