Calculus Problem of the Week – August 5, 2011

Sometimes easy and sometimes hard, our calculus problem of the week could come from any calculus topic. If you really want to get better at calculus, following these problems is a great way to make yourself practice! Past calculus problems of the week.

If you have noticed the date changes lately, I have shifted these from being posted on Monday’s to being posted on Fridays to fit better with when I want to post other types of articles. You will still find the problem right here every week though!

Although I usually don’t like them, this week I have decided to go with a bit of a “trick” question. (I was inspired by some AP questions I saw recently, but this is good no matter what level you are studying at)

This is only a trick question in the sense that if you don’t immediately recognize one important feature, you will probably get it wrong or at the very least do much more work than necessary. If you DO notice it, you will find this is a very routine problem. Hmmm have I now ruined it? Take a look and see how you do.

This week’s problem:
(click “see the solution” at the bottom of post to, well, see the solution.)
Find the derivative of e^3cos(x)

See the solution.

You may be tempted to start off with the product rule here, but that would actually be overkill (it WILL work if you do it right). Instead, notice that e^3 is a constant. Therefore, (e^3cos(x))'=e^3(cos(x))'=e^3(-sin(x)=-e^3sin(x).

As you can see, very routine – pay close attention in calculus to things that LOOK like variables but are actually constants to save yourself from getting the problem wrong or more work than necessary.