So the online source that I found was from HMC and was short, succinct, and easy to read. The examples were really easy for me to understand and the explanations of the Product Rule made sense. I like this better than the textbook which seemed to me to be longer than it needed to be. The "fairly complicated algebra" passed me by and I found that the Property section was all I needed to understand the rule. I definitely feel that the online source was more useful to me.

If I had wanted all the long algebra they gave the link, just in case.

This definition and example come from

http://www.math.hmc.edu/calculus/tutorials/prodrule/

Definition:

h(x)=f(x)g(x)=f(x)g(x)+f(x)g(x) Example:

If

h(x)=x2sinx then

h(x) = =2xsinx+x2cosx = (x2)sinx+(x2)(sinx)
Hi Beston,

ReplyDeleteThe example you chose from the online source is a good one, since it is immediately clear why you would need to use the product rule to take the derivative. The two function in the product are easy to identify.

Mathematicians often as "what if...?" questions as they are exploring new ideas. So here is my question for you: what if you have more than two functions in a product? Does the product rule still apply? Consider the possibility of adding an example which explores this idea.

SKS

Hello Sarah,

ReplyDeleteThank you for commenting, I apologize for taking so long to reply. Your "what if...?" question of whether the product rule still applied or not for more than two functions made me think about a problem on one of our explorations. When I did the problem I made a convoluted attempt at applying the product rule to each function, it didn't work. In class though we went over the problem and I learned that the step is to make the X amount of functions into just two functions.

The problem is:

y=(3x^5)(x^2-4)cos10x

Then make it into two functions:

y=(3x^7-12x^5)cos10x

Find the derivative:

y'=(21x^6-60x^4)cos10x-10sin10x(3x^7-12x^5)

And clean it up:

y'=3x^4[(7x^2-20)cos10x-10sin10x(x^3-4x)

I hadn't considered more than two functions using the product rule, but i guess...it takes two to tango :)

Thanks!

P.S.

I miss you a lot and hope you are having a wonderful time!