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Math Help - derivative of cos^3(3x)?

  1. #1
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    derivative of cos^3(3x)?

    is it -3sin^3(3x) or did i miss something?
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  2. #2
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    Re: derivative of cos^3(3x)?

    Quote Originally Posted by daniels View Post
    is it -3sin^3(3x) or did i miss something?
    Yes you need to use the chain rule. Twice.

    let

    f(u)=u^3

    u=cos(v)

    and

    v=3x

    Then by the chain rule you get

    \frac{df}{dx}=\frac{df}{du}\frac{du}{dv}\frac{dv}{  dx}

    3u^2(-\sin(v))(3)=-9\cos^2(3x)\sin(x)
    Thanks from daniels
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    Re: derivative of cos^3(3x)?

    so then im guessing for f(x) = 2sin(2x) + e^(3x^2) + cos^3(3x)

    f '(x) isn't= 4cos(2x) + 3e^(x^2) + -3sin^3(3x) ????
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    Re: derivative of cos^3(3x)?

    Quote Originally Posted by daniels View Post
    so then im guessing for f(x) = 2sin(2x) + e^(3x^2) + cos^3(3x)

    f '(x) isn't= 4cos(2x) + 3e^(x^2) + -3sin^3(3x) ????
    The derivative of the first term is correct, you need to use the chain rule on the last two terms.
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    Re: derivative of cos^3(3x)?

    okay thnks
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