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Curious about two things..

First, is it possible to use a method such as differentiation from first principles (the whole [tex]lim_{\delta\rightarrow0}\[f(x+\delta)-f(x)]/\delta[/tex] thing) to differentiate trigonometric functions? Or is everyone stumped with memorizing them? (I'm curious about this, I'm not the kind of guy to memorize a formula list or something, I'm curious as to how these forms were found or an alternative method for finding their derivatives)

Next question, how were the short integration formulae found? Is there anything similar to differentiation from first principles for integration?

Excuse me for my lack of knowledge or ignorance for asking such questions.

Thanks.

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# Stupid Question, Curious

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