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  1. W

    Cycloid power series. problem from hell.

    Problem from the sky Ignoring homotheties, let the following cycloid: x = t - sin t y = 1 - cos t, t in [0, 2pi]. From this, we have y' = dy/dx = (dy/dt) / (dx/dt) = (sin t) / (1 - cos t) = ... = cot (t/2), and then y'' = d(y')/dx = ... = -(1/4) [ cosec (t/2) ]^4, ..., "AND SO ON" :rofl...
  2. W

    [For experts] Derivatives of 1/f(x)^2

    Mr. Benorin, you see, this is a local problem: the final result is evaluated at x = a. Besides that, f satisfies some particular conditions, which must be considered: (a) f(x) \neq 0, over some open interval A; (b) f is a series of even powers; (c) f^{(2n+1)}(a) = 0 and f^{(2n)}(a) \neq 0, n...
  3. W

    [For experts] Derivatives of 1/f(x)^2

    It may help Thank you, Mr. Benorin. I'm trying to adapt the Faá di Bruno's formula to my problem. :rolleyes: Bob
  4. W

    [For experts] Derivatives of 1/f(x)^2

    My question is presented in the uploaded pdf file. :surprised