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Math Help - Function inside a function

  1. #1
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    Function inside a function

    Given (d/dx)f(tan(x))=1

    Find f'(x)

    I got up until

    f'(tan(x))=cos^2(x)

    But can't figure a way to take tan(x) away from cos^2(x)
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  2. #2
    MHF Contributor
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    Substitution: u = tan(x) so that x = atan(u).

    This gives: f'(u) = cos^2(atan(u)) = 1/(u^2 + 1)

    It is now a little confusing to substitute back to 'x' (without the tangent), but we'll just have to get past that.
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