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Math Help - taking the derivative of trig functions

  1. #1
    Junior Member TheMathTham's Avatar
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    taking the derivative of trig functions

    Ok, so here is the equation:
    g(x) = (\arccos (x^{2}))^{5}

    I know that \arccos(x) = \frac{-1}{\sqrt{1-x^{2}}}
    We use that for taking the integral of \arccos(x), but to do for the derivative?
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  2. #2
    MHF Contributor
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    You cannot integrate the inverse cosine. To calculate the derivative, use the chain rule:

    g'(x) = 5(\arccos (x^2))^4 * \frac{d}{dx} (\arccos (x^2))
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  3. #3
    Junior Member TheMathTham's Avatar
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    Quote Originally Posted by icemanfan View Post
    You cannot integrate the inverse cosine. To calculate the derivative, use the chain rule:

    g'(x) = 5(\arccos (x^2))^4 * \frac{d}{dx} (\arccos (x^2))
    oh. I see. its not integration, it just allows for substitution. cool. thanks for the help! the answer i got to match my worksheet was -10\frac{x(\arccos(x^{2}))^{4}}{\sqrt{1-x^{4}}}
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