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**LLoyd****Guest**

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

**ryos****Member**- Registered: 2005-08-04
- Posts: 394

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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**irspow****Member**- Registered: 2005-11-24
- Posts: 457

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?!

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

Can anyone say polynomial division?

El que pega primero pega dos veces.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 457

I certainly applaud you ryos, if you brave and energetic enough to do that sort of division on this equation.

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**God****Member**- Registered: 2005-08-25
- Posts: 59

0.03 seconds using the mathematica online integrator.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 457

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.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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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**irspow****Member**- Registered: 2005-11-24
- Posts: 457

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.

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