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What are the two touch points mentioned in ch. 1 that will be covered in Anders (2017), "You Can Do Anything: The Surprising Power of a "Useless" Liberal Arts Education"?
Not all functions are polynomials. You're going to want to use the formal definition to arrive at derivatives for things like sin(x) or ex. Also, you can't even differentiate rational functions if you don't have the quotient rule or at least the product rule on hand.
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