(Photo Credit: http://www.karlscalculus.org/qrule_still.gif)
Fig 1. (Awesome Picture)
Fig 1. (Awesome Picture)
In our exploration, we used the Product Rule in order to derive this rule that tells the derivative of a quotient of two functions. So before we go into that we should do a quick review of the Product Rule.
In Words: Take the derivative of the first function times the second plus the first function times the derivative of the second.
Long Form: 
Short Form: y’=u’v+uv’
Ok, so now that we’ve got the product rule fresh in our minds let’s use it to find the derivative of a quotient property.
Let 
1. 
1. Multiply each side of the equation by v.
1. Multiply each side of the equation by v.
2. 
2. Take the derivative of each side of the equation, applying the product rule to the left side.
2. Take the derivative of each side of the equation, applying the product rule to the left side.
3. 
3. Isolate y’ in the left side of the equation.
3. Isolate y’ in the left side of the equation.
4. 
4. Substitute u/v for y in the numerator of the expression.
4. Substitute u/v for y in the numerator of the expression.
5. 
5. Multiply the numerator and denominator by v and simplify.
5. Multiply the numerator and denominator by v and simplify.
6. 
6. Derivative of a quotient property.
6. Derivative of a quotient property.
And so finally I present you with…
The Quotient Rule!!!
If , where u and v are differentiable functions of x, and v does not equal 0,
, where u and v are differentiable functions of x, and v does not equal 0,
Then
In Words:
The derivative of the numerator times the denominator minus the derivative of the denominator times the numerator, all divided by the denominator squared.
And just for fun, but also for education, here is a video I found that is a catchy tune for remembering this rule.
Well that’s all for today’s lesson. I hope it was helpful and informative. Leave comments and questions!
The next scribe is BlueElephants.
Posts
Love the song!!! very creative!
ReplyDeletedoes anyone have any advice for me on #3 on check your understanding. im having trouble finding the derivative equation. there could be something im not seeing.
gracias
E~~It is always hard to start.
ReplyDeleteFirst, I like the short review of the product rule. That's really neat. However, I think there is a very tiny, tiny error that u and v are not defined. Actually, u and v are defined in the explanation of quotient rule. That is good.
Second, instead of typing out the equations, you used the picture of equations. That is nice. However, some of the equations were typed out; some of them were pictures. I think it would be better if you represent all the equations with picture or just type them out.
Third, "", this kind of things are everywhere in this post. I don't know why this happens. But it would always be a good thing to save your post first and preview it to see whether there are any small mistakes.
Lastly, the post is concise and complete, which is good. However, I think some example questions and solutions are still very necessary to make a better explanation of quotient rule.
By the way, the song is awesome.
It is me again.
ReplyDeleteadd to my comment up there.
I don't why this thing down here doesn't show up in my first comment. And it actually appeared when I did the preview. It is weird.
I don't know if this thing will show up this time.
This goes in after the word third.
And,
one quick question,
Do you think it is ture that if product rule applys in one function, quotient rule could also apply in this function?
This was such an awesome Scribe Post! Setting the bar really high! Well done, I love both the picture and song, so fun.
ReplyDeleteFor future reference, did you create the post in Word or something before posting it, or did you just use the posting box? I was wondering because I really liked the layout of this post, really clean and easy to read. I would love to make mine as easy to read in the future.
This post has a very good definition of the quotient rule and it is helpful to review the product rule as well. I think it would be really good for future posts if you included a few examples of how to use the quotient rule. But otherwise it is beautiful and the video is awesome! Also nice looking equations, did you use the equation editor thing on the homepage of the blog?
ReplyDeleteHi Babar,
ReplyDeleteThis is an excellent scribe post. I was impressed with the organization of the post as well as the clear verbal explanations that supported the algebraic steps.
I agree with YDplusSB that it would be even cleaner looking if you were consistent in your use of either the equations or the pictures of the equations.
Another way to improve the layout would be to use a table (with the borders hidden) for the two columns, one with algebraic manipulations and the other with the supportive words. I'm not sure if this formatting in Word would paste into the post, but it might be worth a try. I use that technique a lot as a teacher.
I like how you included multiple notation forms for the product rule. Do you think it would be helpful to do the same for the quotient rule at the end of your post?
Great job.
SKS
I love the song in this post, it was great, I also thought it was a very thorough review of the quotient rule. I agree with YDplusSB and blitzen in saying that it could have used an example, not a necessary item in my book, but it would be a nice touch. And although I completely understood the deriving of the quotient rule from your explanation, I think that the layout could have been more formatted to have the equations in one row and the explanations in the other. All in all though it was a great post, it is a quality depiction of the work we did in class.
ReplyDeleteI like the song provided on the post, and usage of different color was fresh on this post. The picture you used at the very top also is a well represented picture of the quotient rule. However, i would like to give you several suggestion for your future writing on scribe post. I think it would be better if you use more organized formatting in terms of the layout. Also it is little redundant to use numbers after showing the equation, it is just double used.
ReplyDeleteThe very first thing I liked about this scribe post is the revision about the product rule. I also liked the way you explained each step, giving all of the explanations needed.
ReplyDelete