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Can you explain what rule this is? I'm highly curious as to what rule can solve all derivatives, and it might be useful for me.

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Sure: the line tangent to any point on a smooth curve approximates a sufficiently small bit of the curve surrounding the point arbitrarily well.

Newton's contribution wasn't this, however, but the extension of Descartes' algebraic tangent-finding methods to curves represented by "infinite polynomials", which he neither uses nor explains in the Principia. If you're looking to learn Newton's flavor of calculus "from the master", here it is:

http://archive.org/details/methodoffluxions00newt

f'(x) = lim h->0 (f(x+h)-f(x))/h

If that's the really the rule ekm2 is referencing, the rest of his comment falls apart. This rule is found in the first section about derivatives in any college or high school calculus textbook. They lead you on for a good many pages that calculus problems are actually practically solved by reference to this equation, then grudgingly admit (after forcing you to use it many times) that the power rule, among others, exists.

I assume he's referring to this [1], although Newton invented his calculus because he couldn't use this approach to solve practical problems.

[1] http://en.wikisource.org/wiki/The_Mathematical_Principles_of...

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