# Newton and Leibniz approach to differentiation

1. May 9, 2013

### DeeAytch

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?

2. May 9, 2013

3. May 9, 2013

### DeeAytch

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.

4. May 9, 2013

### Simon Bridge

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.

5. May 9, 2013

### lugita15

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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