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Newton and Leibniz approach to differentiation

  1. May 9, 2013 #1
    Newton and Leibniz both had a method of differentiating. Newton had fluxions and Leibniz had something that resembles the modern derivative.

    Historically, does anyone know how they went about calculating the derivative?
     
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  3. May 9, 2013 #2

    Simon Bridge

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  4. May 9, 2013 #3
    Thank you for responding.

    I am looking specifically for examples of the algorithms as they were employed historically. If nobody can provide that, then I suppose I'll dig through the sources you listed.
     
  5. May 9, 2013 #4

    Simon Bridge

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    Both authors had long careers in which they employed their respective techniques via a range of actual processes or algorithms which they developed as they went. The references provide access to a range of examples - you'll see what I mean quite quickly. Good luck.
     
  6. May 9, 2013 #5
    Here is the infinitesimal definition of the derivative that Leibniz (and Newton implicitly) used: df = f(x+dx) - f(x), and df/dx = (f(x+dx) - f(x))/dx. For instance, if f(x) = x^2, then df = (x+dx)^2 - x^2 = 2xdx + dx^2, and then you get rid of dx^2 because it's the square of an infinitesimal, so it's infinitely smaller than 2xdx. Thus we have df = 2xdx, so df/dx = 2x.
     
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