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Math Help - Derivative question.

  1. #1
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    Derivative question.

    Is this right?

    y=cos^{-1}(cos(x))

    So

    \frac{dy}{dx}cos^{-1}(cos (x))=1

    I figure this as (I'm not sure if my working here is flawed or not)

    \begin{align*} y&=cos^{-1}(cos(x))\\cos( y)&=cos(x)\\y&=x \end{align*}

    And I also did it via substitution and got the same answer. I googled

    \frac{d}{dx}cos^{-1}(cos (x))

    though and there are a few different answers....none of them mine.
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  2. #2
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    Re: Derivative question.

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  3. #3
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    Re: Derivative question.

    Ok I see where I went wrong in my my substitution working.

    So

    \frac{dy}{dx}cos^{-1}(cos(x))=\frac{sin(x)}{|sin(x)|}
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