I thought that the textbook gave a good explanation of the product rule. The examples of the product rule being done on functions was easy to follow and it had a box stating the product rule verbally.

"Derivative of first times second, plus first times derivative of second..And don't forget the chain rule". Although the textbook was good, the site I found was really nice because it had figures that moved and showed the product rule in affect. The figure showed the relation the two functions and their derivatives and you could manipulate the components. Overall, I liked the site better because of the figure but if I had not read the textbook first, I may have not understood the site as much. The product rule as the site stated, is

{**f**(x)*g*(x)}^{'}=*f*(x)*g*^{'}(x) +*f*^{'}(x)*g*(x).

ex. y = x^{2}(3x+1)

First you take the derivative of the first equation (2x) multiplied by the second, which equals 6x^2+2x

Plus the derivative of the second equation (3) multiplied by the first, which is 3x^2

and it all comes out to 9x^2+2x.....I think

Let me know if this is right!

Textbook does provide better definition of the Product Rule. I like your usage of thicker letters to represent the definition of the product rule. Also, the answer provided for your example is correct; however, just a small suggestion, i think it is better to use the example that can only be solved with product rule.

ReplyDeleteHey J-tron foteen, I like the example you provided in your post. Like Hyunhwa commented, the derivative can be found in another way, too... it would be neat if you could show us how to do it the alternative way and then show that the two answers match! (Hint: try distributing the x^2 first). I have to disagree with Hyunhwa, though, because providing an example like yours (that can be solved in more than one way) makes it easier for me to verify that the Product Rule isn't just nonsense... it actually works!

ReplyDeleteAlso, which website did you use to learn more about the Product Rule? I'd love to check it out...

Thank you for verifying that my answer was right. I see what you mean Cary, after you distribute the x^2, you can use the power rule to get the same answer. Thanks for mentioning that and here is a link to that site. http://www.ies.co.jp/math/java/calc/seki_bib/seki_bib.html

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