Product rule:
If f and g are differentiable functions, then the derivative of the product fg is:
(fg) '(x) = f(x) g '(x) + g(x) f '(x)
Sunday, January 10, 2010
Product Rule for visual Learners
When searching the internet for the product rule i stumbled upon a Youtube video. As a visual learner, i found it very helpful because the man gave an easy (non mathy) way to understand the procedure of the power rule. Also it allowed me to watch and listen to someone solving equations. However, the textbook gave a much more in depth explanation of what the Product Rule is. I found that the textbook was better for understanding the concept, but the video was much more helpful for explanations.
Example: f(x)=g(x)(h(x)) f(x)=5x^3sin4x f'(x)=(15x^2 (sin4x))+(4cos(4x)(5x^3))
link:http://www.youtube.com/watch?v=uPCjqfT0Ixg
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Hey Tubby, I'm your mentor! Finding a visual resource was a great idea, I'm glad it helped you. I always get a lot out of seeing how other people do problems.
ReplyDeleteI think you could make your post stronger by taking another look at your example. In order to demonstrate the product rule the function you are differentiating must really clearly be the product of two other functions. Take another look at your function and check if it is a product of two functions - what are they? It might help in your example to explain for the reader what the two functions are - maybe label them f and g like in your product rule definition?
Great start!
I added the separate functions, i think thats how they are split up, is this what you were suggesting?
ReplyDeleteTake a look at your definition again. Notice that f and g are multiplied together (it is, after all, the product rule). Now look at your example. Is f(g(x)) the same thing as (fg)(x)?
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ReplyDeleteI think i got it, i didn't simplify because if this is wrong i didn't want the algebra to confuse me. But i think the example works now.
ReplyDeleteOoo! You're so close! Check your use of the chain rule, but otherwise you're right on (assuming the large X means multiply?).
ReplyDeleteThe next step for you is to learn how to use the Equation Editor. Its in the right column, and it looks hard, but you just need to play around with it a little. That'll help you make your math look pretty, which will make it easier for you to find mistakes!
Thanks for sticking with me and figuring it out!
Hi Tubby. I too found the textbook to have a good explanation of the product rule. Your example was a bit hard to follow. Maybe some labels or explanations of how you did it would help. The video was nice. It made the product rule really understandable. The dudes voice flows well and his whiteboard brings it all into perspective. Nice job!
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