The Morning's Issues

This morning I ran into an issue while working on "related rates" problems. Well, two issues, really.

The first was that I found I had a poor understanding of how to differentiate equations with respect to a variable (time, in these cases) that was not part of the equation itself. I found a clear explanation of what I was missing in the book How To Ace Calculus: The Streetwise Guide which, despite the title, is really a good book.

Example(s) forthcoming (see below).

Second, I discovered that I did not know how to extend the product rule to more than two functions. That is, I did not know how to differentiate

y = f(x) * g(x) * h(x)

Unless I missed it, Thomas/Finney does not cover this until later in the same exercise set. This is disconcerting because overall I am finding this text to be pretty good.

My gripe with this is double: 1) covering something after it is needed, and 2) covering it in an exercise set. Suppose you were not assigned or otherwise don't do that exercise? I guess you get to look it up, like I did.

Once I started to think about posting, I realized I did not know how to properly format mathematical equations in Blogger. It turns out that this is ... an issue. There are ways to do it, certainly, but it looks as though it will require some larnin'.

MathML might be the easiest way to do this. I will be trying it out.