first six chapters of an introductory text such as the idea that “velocity” is the slope of the tangent to a distance-time curve, or that “rate” is the slope of the tangent to some other kind of curve. (See, [*e.g.*]{} excerpts from a proposed text at http://www.hep.anl.gov/jlu/index.html.) It also omits such vital topics as the product and chain rules.

Section 3 uses the dibbl method to obtain the derivatives of the sine and cosine functions. I believe that the derivation presented here is novel (for a textbook), and is much easier to understand and reproduce than the presentations in other texts. I deliberately omit, in that Section, any discussion of uniqueness. “Less is more”, especially in introductory textbooks.

I simplify the language by speaking of the [*slope of a curve*]{} when I mean the [*slope of the tangent to the curve*]{}.

 FINDING SLOPES
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> Your Majesty says, “Kill a gentleman, and a gentleman is told off to be killed. Consequently, that gentleman is as good as dead - practically, he is dead - and if he is dead, why not say so? ”[*The Mikado, Act II*]{}, by Gilbert and Sullivan

I motivate the derivative, as pointed out in the 