Doing It With e
This blog is all about a problem I had with e.
There you are jumping to conclusions again! I’m not talking about the drug you get at raves. I’ve never actually tried that kind of e, though guys have offered it to me. Diet Coke and chocolate are my drugs. 🙂
No, I’m talking about Euler’s number e, which is about 2.71828.
I’ve always been a little scared of e. And horses. And spiders. Don’t ask me what all those things have in common, except that they all scare me.
I recently got a math problem wrong because of e, and I just wanted to share my mistake in case anyone else gets confused like I did.
Calculus books (including mine and a couple others that I looked at) say that when you take the derivative of e, you get the same thing:
And that’s true. Kind of. If you’re not careful, it’s how you will remember the rule. That’s where I went wrong.
What makes it confusing is that the book is showing you a special case. Some books don’t make that clear enough. The derivative of x with respect to x is 1, so what you actually get is:
I hate to admit making a stupid mistake, but maybe I can help other people avoid it. When you differentiate e, the actual rule is this:
In other words, you differentiate the exponent (whatever it is) and then multiply that times e raised to the original exponent.
This blog probably isn’t as much fun as arguing about health care reform, but it’s a lot more useful if you’re a student.
Copyright 2010 by Rinth de Shadley.