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: