tag:blogger.com,1999:blog-7806043650549721218.post1759773253986449191..comments2019-10-11T09:45:41.680-05:00Comments on EPSILON-DELTA: More thoughts on the Chain RuleRebecka Petersonhttp://www.blogger.com/profile/12227797437296056645noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-7806043650549721218.post-18948766103577670012012-08-14T12:33:38.001-05:002012-08-14T12:33:38.001-05:00Oooo I like plugging in a number for the ind. vari...Oooo I like plugging in a number for the ind. variable. That's something concrete I can use when students are struggling with identifying the inside and outside functions. Brilliant!Rebecka Petersonhttps://www.blogger.com/profile/12227797437296056645noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-58753659159019028722012-08-13T19:50:18.158-05:002012-08-13T19:50:18.158-05:00Also you can probably tell I'm working through...Also you can probably tell I'm working through my backed up google reader :)Bowmanhttps://www.blogger.com/profile/12131274143375221111noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-82902748738225195112012-08-13T19:49:13.632-05:002012-08-13T19:49:13.632-05:00Hey I had very similar problems with my students. ...Hey I had very similar problems with my students. The last thing you pointed out in your comments was the thing that really helped. Some still had trouble with e to a function though. One thing that helped with that was asking them to plug in 5 or some other random number (by hand, not with the calculator). Then they can see what they do... Oh you do the stuff in the exponent first, then take e to the whole thing. So e has to be the noutside function, or the second function.Bowmanhttps://www.blogger.com/profile/12131274143375221111noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-24858179240043447932012-08-01T11:07:20.418-05:002012-08-01T11:07:20.418-05:00Exactly! They seem so comfortable with the square...Exactly! They seem so comfortable with the square root function. I don't know why I didn't think of this before, but maybe giving them f(x)=sqrt(x^2+1), f(x)=sin(x^2+1), and f(x)=ln(x^2+1) all in a row will help. Keep the inside functions the same for the first example. Thanks, Sue!!!Rebecka Petersonhttps://www.blogger.com/profile/12227797437296056645noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-72534339613286391402012-08-01T10:57:33.419-05:002012-08-01T10:57:33.419-05:00You may be right, but I'd blame it more on not...You may be right, but I'd blame it more on not understanding functions themselves, rather than on not understanding composition. A way to test my hypothesis would be to ask them to give the derivative of the square root of (x^2+1). They've dealt with square roots for much longer than they've dealt with trig or logs. Plus, it doesn't have the parentheses that make them think 'multiplication' (!). OK, I have to remember this, I'm going to quiz mine in the fall on 3 functions: a square root, a trig function, and a log. Each will have a simple function of x inside.<br /><br />We know that teacher said, "e is just a number". I say it all the time. I never imagined a student would/could misremember it this way!Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-48060719563508242222012-08-01T10:50:37.682-05:002012-08-01T10:50:37.682-05:00Sue--
Oooo! I like the onion analogy! Stealing ...Sue--<br /><br />Oooo! I like the onion analogy! Stealing it. :)<br /><br />I thought it was a log issue as well, until I got similar responses for trig functions, too. For example, we had an expression such as x+cos(2x), and a student asked why we can't factor out an x (and this wasn't an isolated comment). It was comments like these that made me think a lot of students don't just "see" the inside function. What's been your experience with composite functions?<br /><br />Also, when I was helping a student one-on-one with derivatives of log functions, he made the comment, "But my College Algebra teacher told me ln is just a number." Which, surely didn't happen, but really got me thinking...it seems like there's some kind of disconnect for compositions that isn't there for the other 4 combinations of functions.Rebecka Petersonhttps://www.blogger.com/profile/12227797437296056645noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-3804260916432623782012-08-01T10:45:15.281-05:002012-08-01T10:45:15.281-05:00Hay dude yes the chain rule very difficult, thanks...Hay dude yes the chain rule very difficult, thanks for the share. <a href="http://www.sampleproposal.org/product-proposals.html" rel="nofollow">Product Proposals</a>Lisahttps://www.blogger.com/profile/09680687232989598778noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-66527701773844571122012-07-31T13:44:07.079-05:002012-07-31T13:44:07.079-05:00My guess is their problems were more with the loga...My guess is their problems were more with the logarithm function than with chain rule. So I'd review logs too.<br /><br />For chain rule, I try to get them to use the word something as much as possible to see the structure of an expression:<br />log of something<br />something times something<br />something to the something power<br />square root of something<br /><br />And I talk about the chain rule helping them to peel off the outer layer first, like an onion.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com