Saturday, July 12, 2008

Different Dots!

I wonder if people really know what differentiation is? What does this monster of a “dee-wai-dee-axe” mean to everyone? To be frank, there are so many sides of differentiation that I can’t put my finger down on an exact meaning that fits the nature of differentiation. Differentiation is simply one of the most beautiful tools in mathematics that allows you to obtain wonderful relations.

Differentiation, to Richard Feynman, was a game; he allowed for the convention:

And then differentiation was reduced to nothing but a mere game of placing the dots:

Differentiation has never been easier! Dot placing has been the most interesting way to do differentiation:

And it’s all about playing with dots. Sometimes one dot, sometimes two! But it’s all about using dots efficiently. I’ve just illustrated an extended version of the product rule in differentiation. I very much like to call it the ‘dot’ rule.

How about the quotient rule? Well, that’s easy! Looky here:

And if I put it altogether, we have:

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