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## #1 2006-02-04 05:54:50

LLoyd
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### 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 2006-02-04 06:22:59

ryos
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### 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.

## #3 2006-02-04 09:05:58

irspow
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### 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?!

## #4 2006-02-04 09:28:29

ryos
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### Re: Quotation and Chain Rule HELP

Can anyone say polynomial division?

El que pega primero pega dos veces.

## #5 2006-02-04 09:48:01

irspow
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### 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.

## #6 2006-02-06 13:16:45

God
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### Re: Quotation and Chain Rule HELP

0.03 seconds using the mathematica online integrator.

## #7 2006-02-07 10:37:26

irspow
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### 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.

## #8 2006-02-07 14:34:22

Ricky
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### 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..."

## #9 2006-02-07 15:00:52

irspow
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### 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.