Or textbook clearly explained the definition of the derivative of a product of two functions. It also gave three examples in order to fully understand the product rule. The book includes both a mathematical and verbal explanation. The online explanation was similar in that it mathematically explained the product rule and gave multiple examples. I found the online explanation useful in that it explained the product rule in terms of f(x), g(x), and h(x), mathematically in multiple ways. I found the textbook explanation a bit easier to understand and visualize because of its verbal explanation.

Product Rule: Mathematical: If h(x)=f(x)g(x), then h'(x)= f'(x)g(x)+f(x)g'(x),

Verbally: The derivative of the function of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second.

Example:

f(x)=x^{4}cos6x

f’(x)=4x^{3}cos6x+x^{4}(-sin6x)(6)

f’(x)=4x^{3}cos6x-6x^{4}sin6x

Hi BlueElephants, I'm your mentor. Solid post here, I like that you identified the different ways that the book an the website presented the information (what was the website - can you give us a link?). I like that you used two methods in your definition of the product rule as well. I want to challenge you to tighten up your verbal explanation a bit, I think you could be more clear there. Maybe use more than one sentence? Also, since the verbal explanation was helpful to you in the textbook, can you add verbal explanation to your example?

ReplyDeleteGreat start.

Thank you for the advice. The link that I used was: http://www.math.hmc.edu/calculus/tutorials/prodrule/. The verbal definition included in my example was nearly the same as the one in the book. I added a few words to clarify the definition in my mind. The book’s definition stated “The derivative of the function of the product of two functions is the derivative of the first times the second plus the first times the derivative of the second." I will make sure to keep working on tightening my verbal explanation and when I finish it, will post it.

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