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#1 2006-02-03 06:54:50
- LLoyd
- Guest
Quotation and Chain Rule HELP
Hi everybody, can you help me solve this:
y = (2x+1 / 3x-2)^5
find dy/dx using the quotation and chain rules.
ive got an answer but i think i got confussed during the quotation rule.
Thanks
#2 2006-02-03 07:22:59
- ryos
- Member
- Registered: 2005-08-04
- Posts: 394
Re: Quotation and Chain Rule HELP
y′ = 5(2x+1 / 3x - 2)^4 * [ (3x-2)2 - (2x+1)3 ] / (3x-2)²
= 5(2x+1 / 3x - 2)^4 * -7 / (3x-2)²
El que pega primero pega dos veces.
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#3 2006-02-03 10:05:58
- irspow
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- Registered: 2005-11-24
- Posts: 1,055
Re: Quotation and Chain Rule HELP
Yes, but could you imagine being given:
560x^4 + 1120x^3 + 840x^2 + 280x + 35
81x^4 - 216x^3 + 216x^2 - 96x + 16
And have to integrate it back to something resembling what we have above?!
I am at an age where I have forgotten more than I remember, but I still pretend to know it all.
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#4 2006-02-03 10:28:29
- ryos
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- Registered: 2005-08-04
- Posts: 394
Re: Quotation and Chain Rule HELP
Can anyone say polynomial division?
El que pega primero pega dos veces.
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#5 2006-02-03 10:48:01
- irspow
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- Registered: 2005-11-24
- Posts: 1,055
Re: Quotation and Chain Rule HELP
I certainly applaud you ryos, if you brave and energetic enough to do that sort of division on this equation.
I am at an age where I have forgotten more than I remember, but I still pretend to know it all.
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#6 2006-02-05 14:16:45
- God
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- Registered: 2005-08-25
- Posts: 59
Re: Quotation and Chain Rule HELP
0.03 seconds using the mathematica online integrator.
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#7 2006-02-06 11:37:26
- irspow
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- Registered: 2005-11-24
- Posts: 1,055
Re: Quotation and Chain Rule HELP
Sorry, God. I am an old guy and have a tendency to want to do things by hand. Whenever I use my TI-89, I almost feel like I'm cheating in some way. But if you really need an answer there is nothing wrong with using technology to find the answer. Actually, I use my calculator all of the time, it's not like I sat down and memorized the trigonomic tables....hmm, I have to put that on my to-do list.
I am at an age where I have forgotten more than I remember, but I still pretend to know it all.
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#8 2006-02-06 15:34:22
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Quotation and Chain Rule HELP
it's not like I sat down and memorized the trigonomic tables....hmm, I have to put that on my to-do list.
Which is only second to memorizing The On-Line Encyclopedia of Integer Sequences
.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#9 2006-02-06 16:00:52
- irspow
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- Registered: 2005-11-24
- Posts: 1,055
Re: Quotation and Chain Rule HELP
I didn't mean every fractional degree. Just maybe every degree of sine up to forty-five for example. You wouldn't have to do cosine or tangent because of the relationships among them.
A list of forty five numbers, to an accuracy of my choosing, wouldn't be that hard. I memorized the first five hundred digits of pi over ten years ago and I can still write them down on a piece of paper if I had to. There are many different ways to remember long numbers and lists, some techniques dating back to ancient Greece. Ironically, they don't bother teaching these techniques to school children.
I am at an age where I have forgotten more than I remember, but I still pretend to know it all.
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