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    Real Analysis Problem

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    The inverse cosine function has domain [-1,1]and range [0, pi]. Prove that (cos^-1)'(x) = -1/ sqrt(1-x^2).

    This needs to be proved from a real analysis point of view not a calculus.

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    https://brainmass.com/math/real-analysis/inverse-cosine-function-domain-9539

    Solution Preview

    Let y = cos^-1(x)
    <br>
    <br>So now we need to prove that dy/dx = -1/sqrt(1-x^2)
    <br>
    <br>Let x = cos(t)------eqn 1
    <br>
    <br>Therefor y = cos^-1(cos(t))
    <br> or y = t (because cos^-1 of cos means just ...

    Solution Summary

    The inverse cosine functions of domain are analyzed. The expert proves from a real analysis point of view not a calculus.

    $2.49

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