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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. ๐Ÿ™‚

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.

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  1. David
    March 10, 2010 at 12:34 am

    In old-fart terms, please? Think someone at least 20 years out of calculus…

    Hey, at least I can make change and run a crank-powered cash register! ๐Ÿ™‚ No I wasn’t the crank…

    A joke, totally off subject: A Catholic man, the typical Catholic man who doesn’t go to church except on Easter, was out hunting in the woods. He fell asleep, and woke up with the hot breath of a bear staring him in the face…Well in such situations, we all turn to God…”O Lord, please…make this bear a Christian bear and I’ll go back to church…to which he heard “Bless us O Lord in these thy gifts…”

    • Rinth de Shadley
      March 10, 2010 at 2:39 am

      Hi David —

      You’re not an old f***, but the ideas are really simple. The derivative is just the rate at which something changes. So if you can make change, you know about calculus!

      That’s a great joke. At least the bear was thankful for its dinner. ๐Ÿ™‚

  2. March 11, 2010 at 5:41 am

    But, isn’t this just the chain rule?

    I’ve never seen square brackets used for the derivative, where did you get it from?

    • Rinth de Shadley
      March 11, 2010 at 1:23 pm

      Hi Lucky —

      It sure is the chain rule. Like I said, it’s a stupid mistake. But I’m not the only one who made it, so I thought it was worth talking about. ๐Ÿ™‚

      Thanks for the great comment!

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