Today I just googled 'product rule' and looked at one of the options that came up. From just looking at one site, I understood the product rule. The site I looked at: first gave a verbal definition and also an algebraic definition. Then, it had a whole list of problems that you could look at a detailed solution to. It included all kinds of problems full of exponents, trig, ln, etc. Also, in the solutions, each step was clearly written out and it was easy to see what had been done. When I looked at the book, however, I was confused, even though I had just learned the product rule. The verbal descriptions it had were very complex and confusing and I could not follow them. One thing I didn't like about the web site I found, though, was that there was not a verbal description for each of the steps in the solutions, which the text book offers. It helps me to see example with real numbers instead of just variables, but it also helps me to read how each step was done.
Definition:
if h(x)=f(x)g(x)
then h'(x)=f'(x)g(x)+f(x)g'(x)
Example:
if: h(x)= (x^2+5)(3x)
then: h'(x)= (2x)(3x)+(x^2+5)(3)
(derivative of the first)(the second)+(the first)(derivative of the second)
=3x^2+6x^2+15
=9x^2+15
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Its great to see that you found such a helpful site that provide a number of clearly illustrated step by step examples. However i would really like to know what this site was called so that i could use it for future reference. Also i really i like your use of the if, then stuff in your definition and example portions of you last post. Thanks
ReplyDeleteHey Secret, I'm your mentor.
ReplyDeleteYour analysis of the various sources you used was interesting, sometimes writing a verbal description is hard. I want to challenge you to add that to your post since you thought it was helpful. Can you add verbal descriptions to your example? Also, just check over your example again, you've got a small error.
I agree with Winn Plot, nice use of If...Then!
Thanks for the comments! I just realized that I commented on someone else's asking them to include the link also...and I didn't even do it in my own. Oops. I think I fixed the example.
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