The Product Rule

AP Calculus AB· difficulty 3/5

If f(x)=exsinxf(x) = e^x \sin x, then f(x)=f'(x) =

  • A

    excosxe^x \cos x

  • B

    exsinxcosxe^x \sin x \cos x

  • C

    ex(cosxsinx)e^x(\cos x - \sin x)

  • D

    ex(sinx+cosx)e^x(\sin x + \cos x)

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Explanation

exsinx+excosx=ex(sinx+cosx)e^x \sin x + e^x \cos x = e^x(\sin x + \cos x).

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