Tuesday, 19 April 2005, 14:11:34 EDT
I have started making a list of the things I want to write about in my experience with my Apple PowerBook. I want to cover everything and I want to make sure that what I write is fairly accurate. That is why I haven't made much mention of it since I acquired the machine. I don't want to do one of those "month with a Mac" or, as OSNews thinks to be relevant, "two days" with a Mac article. Thus far though, I am really digging the system and find more reasons to like it every day; in fact, I just found a neat trick using Exposé while composing this post. It will be a while yet before I write my article. I just ordered the next version of OS X and I want to include that in my article.
Here is a differentiation problem that I think is really neat. I just worked it out and realized I got it completely wrong the first time I worked it about a month and a half ago.
Let (x) = (x - 1) * (e^x). Differentiate (x) with respect to x. So, '(x) = [(x - 1) * dy/dx(e^x)] + [(e^x) * dy/dx(x - 1)] = [(x*e^x - e^x) + e^x] = (e^x)(x - 1) + (e^x).
Now, differentiate '(x) with respect to x. This results in (read " double prime") ''(x) = (e^x)(x - 1) + 2(e^x). Can you guess what the third derivative of (x) will be? How bout the twentieth derivative?