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Math Help - derivative

  1. #1
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    derivative

    cos^2(1-2x+x^2)

    would this be sin^2(1-2x+x^2)*(-2+x^2)?
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  2. #2
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    Quote Originally Posted by Asuhuman18 View Post
    cos^2(1-2x+x^2)

    would this be sin^2(1-2x+x^2)*(-2+x^2)?
    No! - 2 \cos(x^2-2x+1) \sin(x^2-2x+1) (2x-2) .
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  3. #3
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    Quote Originally Posted by Danny View Post
    No! - 2 \cos(x^2-2x+1) \sin(x^2-2x+1) (2x-2) .
    could you please tell me how you got this?
    thanks
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  4. #4
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    Quote Originally Posted by Asuhuman18 View Post
    could you please tell me how you got this?
    thanks
    If y = \cos^2 (x^2-2x+1) then let u = x^2-2x+1 so y = \cos^2 u. Let v = \cos u so y = v^2. Now the chain rule

     <br />
\frac{dy}{dx} = \frac{dy}{dv} \cdot \frac{dv}{du} \cdot \frac{du}{dx}<br />

    Put in the pieces and back substitute.
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