The Quotient Rule
In the last section I broke from form a little by actually working out the proof step by step. I may do this in the future again, but for this section I’ll leave it to the book.
Using similar reasoning to last time, we can come up with a way to deal with derivatives of two functions of the same variable.
Here’s the rule for quotients:
Now, let me tell you why I don’t like the quotient rule.
First off, a quotient is just a different version of a product. f/g can always be changed to f*h, where h=1/g. It might strike you that handling 1/sin(x) is difficult, but after we do the chain rule in 3.4, it’ll seem easy.
Second, with all that in mind, the quotient rule is kind of a bitch to memorize.
Whereas it’s not typically useful, AND it’s a pain to memorize, AND it’s more a tool (as opposed to a deep mathematical truth), I say fuck it. If anyone can tell me why I should not say so, please explain it to me in the comments.
Thus, in my ever so humble opinion, you should only bother with the quotient rule if you’re going to need it for exams. Otherwise, the chain rule is faster and easier.
Next stop: Trig.