ABSTRACT
This chapter describes a set of ‘power tools’ that will make it possible for the reader to perform tasks that couldn’t be accomplished ‘by hand’ using the methods encountered up to this point. For differentiation, the chain rule, the product rule, and the quotient rule are vital for slicing their way through an array of more complex functions. Similarly, rule for changing the variable of an integral provides just the sort of heavy lifting gear that is necessary for shifting weighty integration problems. The basic sine and cosine functions have an intriguing complementary relationship, but to perform calculus with more useful forms of trigonometric functions. The first new tool makes it possible to differentiate a pair of ‘nested functions’ – but to demonstrate what this term actually means, concrete application is needed. Acetic acid is the active component of table vinegar and the major biological precursor of cholesterol. It is also ejected by whip scorpions as chemical defense against attackers.
