A few days ago,i stumbled on Newton's Principia in my college library, and i could not help noticing how accessible he was relative to his pupils.On the very first page,he gives only one rule for finding derivatives that applies in ALL cases plus worked out examples on how it works.I felt like i had wasted too much of my time in college reading too many useless tomes.
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:
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.
