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#1 2014-01-27 00:35:01

ninjaman
Member
Registered: 2013-10-15
Posts: 43

logarithmic differentiation

hello,

i have this, y = (x+1)(2x+1)^3/(x-3)^1/2

i got

dy/dx = (x+1)(2x+1)^3/(x-3)^1/2 [1/x+1 + 3/2x+1 - 1/2(x-3)]


im not sure about this?

thanks
simon:)

Last edited by ninjaman (2014-01-27 00:35:46)

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#2 2014-01-27 02:35:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,482

Re: logarithmic differentiation

Hi;

Is this what you had to start?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2014-01-27 06:34:18

ninjaman
Member
Registered: 2013-10-15
Posts: 43

Re: logarithmic differentiation

no the bottom bit is (x-3)^1/2

i dont understand how that square root comes about

cheers

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#4 2014-01-27 07:44:11

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: logarithmic differentiation

hi Simon

Those two expressions are the same.

because

Now back to the question:

This expression has 'everything' ; a product, a quotient, and a function of a function so I'll split up the problem a little.

Let's call that y = P/Q where P and Q are the above expressions that make up the fraction.

By the quotient rule:

So lets work out dP/dx

By the product rule

Substituting this in the above:

factorising

That was very tricky and may contain one or more errors.  I will take a break and then come back and check it (if Stefy doesn't beat me to it of course smile )

Checked at 21.09 gmt and one error found and corrected.

Bob

Last edited by bob bundy (2014-01-27 09:45:19)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2014-01-27 10:02:16

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 615
Website

Re: logarithmic differentiation

@bob bundy shame

Thread title wrote:

logarithmic differentiation

Now carry on from here …

Last edited by Nehushtan (2014-01-27 10:56:26)


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#6 2014-01-27 23:48:30

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: logarithmic differentiation

hi Nehushtan

You may have a point.  dizzy

Exercise for anyone with the will to try it:

Show that method leads also to my answer.


Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2014-01-28 00:35:39

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 615
Website

Re: logarithmic differentiation

Well, I think the OP made a slight mistake.

ninjaman wrote:

dy/dx = (x+1)(2x+1)^3/(x-3)^1/2 [1/x+1 + 3/2x+1 - 1/2(x-3)]

I think it should be

dy/dx = (x+1)(2x+1)^3/(x-3)^1/2 [1/x+1 + 6/2x+1 - 1/2(x-3)]

Last edited by Nehushtan (2014-01-28 00:36:07)


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#8 2014-01-28 01:14:48

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: logarithmic differentiation

hi Nehushtan

Thanks.  You have answered his original question and cleared up for me what that first post said.  If it's not been 'Latexed' I find it very hard to follow, especially when the equation is a long one.  I just ignored that and worked from bobbym's post 2.

OK, I've learned my lesson: "Read the question"; but I have also paid the price:  I slogged through it the other way.  Made my brain hurt.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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