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#1 2012-11-15 13:33:05

BarandaMan
Guest

Really Difficult Differentiation! Help please!

i49.tinypic.com/ose3v5.jpg

Ok, as you can see, I did the first bit correct....

The second part with respect to Pi, I cannot get. I have spent over 75 minutes trying. I wrote it down all neat here and took a photo. Please, please, please can you show me in detail how to differentiate this? I am so bad at differentiation and it will really help.

#2 2012-11-15 14:14:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi BarandaMan;

I am sorry but I can not see that. It is showing up very dark on my browser.

I have so far:

that is all I can make out.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-11-15 14:45:09

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi BarandaMan;

I am sorry but I can not see that. It is showing up very dark on my browser.

I have so far:

that is all I can make out.

Thank you! You are right so far!! The end is -1/yLi^y

I have differentiated with respect to Li correctly. The correct answer when differentiating with respect to Pi is on the sheet (let me know if you cannot see it). I cannot do it though, wrt Li I can do though!!

#4 2012-11-15 14:58:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

There is a capital y in the other term. Do you have Y and y?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#5 2012-11-15 15:08:57

Karimazer1
Guest

Re: Really Difficult Differentiation! Help please!

Yes exactly, the little y is meant to be gamma so treated differently from the big Y! big_smile

#6 2012-11-15 15:15:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

So this is what we have:

You can expand that to:

The first two terms are just constants and disappear, you should be able to differentiate the next two terms wrt Pi.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#7 2012-11-15 20:52:07

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

I can do the fourth term as the Pi just dissappears right?

I have no idea how to use the chain rule here when there are fractions and powers like that, I've never seen a function like this before. Please can you help?

#8 2012-11-15 20:56:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

If you mean this term

Simplify it to:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9 2012-11-15 23:47:52

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;

If you mean this term

Simplify it to:

Thank you bobby, how/why does that rule work?

So Pi^-n * Pi = Pi^1-n? (With the divided by P excluded). Why does that work? How? Is this always the case?
Thanks

#10 2012-11-16 01:11:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

When you multiply like that you can add the powers provided the base is the same.

Yes, it is always the case.

http://www.mathsisfun.com/algebra/exponent-laws.html


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11 2012-11-16 08:18:14

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

Ok thank you for all your help bobby. I really cannot do this.

If anyone is willing to post a solution to the differentiation with respect to Pi, please let me know and explain. It may seem like I am not making an effort but I have, a lot, and me posting my working on here will be really unhelpful.

#12 2012-11-16 10:42:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

I can post a solution but I think you need some help with applying the power rule. We can go over it term by term...

This is the derivative with respect to Pi.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#13 2012-11-24 02:24:16

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;

I can post a solution but I think you need some help with applying the power rule. We can go over it term by term...

This is the derivative with respect to Pi.

Thanks. I have tried for days to work this out but I still do not understand this at all. Also, the P^2 on the bottom is inconsistent with the answer from the book. We want to differentiate only with respect to the Pi, not with respect to the 'P' on the bottom....this is completely different to the answer? Now I have two things I don't understand lol:P

#14 2012-11-24 02:57:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;


For the next term let's simplify it a bit before differentiating

Is that clear to start?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#15 2012-11-24 04:47:49

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;


For the next term let's simplify it a bit before differentiating

Is that clear to start?

Yes! Thank you! That all makes sense, except for the last line, I don't know where the divided 'P' has gone?

#16 2012-11-24 04:50:10

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

Basically I understand that Pi^-n bit, but not how ((Pi/P)^-n) / P gives P^ n-1?

So ((1/P)^-n )/ P ? I don't get how to manipulate this! Thank you bobbym.

#17 2012-11-24 10:23:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

When you have an expression like:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#18 2012-11-25 03:51:23

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;

When you have an expression like:

Ok I know we haven't even started differentiating and I can't do this.


So (Pi^-n / P^-n) / P ... so the top stays the same... Pi^-n and the bottom I do not understand? Please can you just explain so I understand??:P It's taking me 5 days to do one question Maths is so difficult and I try so hard.

#19 2012-11-25 03:52:33

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

Can someone just please explain why (Pi/P)^-n / P gives P^1-n... please  someone?

#20 2012-11-25 03:53:31

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

EDIT ^^ why it gives P^n-1..please someone this isn't even the question I wanted to solve in the first place and now I am stuck just simplifying things

#21 2012-11-25 03:56:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

please someone this isn't even the question I wanted to solve in the first place and now I am stuck just simplifying things

Simplifying is supposed to make things easier, it is part of math. Without it some problems are impossible.

It's taking me 5 days to do one question Maths is so difficult and I try so hard.

Pardon me for saying but you come in for 30 seconds and then I do not see you for 2 days. 5 x 30 seconds is 2 and half minutes of time spent on this problem. I could not solve it that quickly either. In order to get something out of this you have to spend the time in here with me, asking questions.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#22 2012-11-26 03:38:10

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;

please someone this isn't even the question I wanted to solve in the first place and now I am stuck just simplifying things

Simplifying is supposed to make things easier, it is part of math. Without it some problems are impossible.

It's taking me 5 days to do one question Maths is so difficult and I try so hard.

Pardon me for saying but you come in for 30 seconds and then I do not see you for 2 days. 5 x 30 seconds is 2 and half minutes of time spent on this problem. I could not solve it that quickly either. In order to get something out of this you have to spend the time in here with me, asking questions.

Ok. Thank you for your reply. That is a very helpful breakdown and it makes sense. I have been trying a lot but just keep getting nowhere so come back to ask questions. Sorry. sad

Ok, so I understand how to simplify the term, so now can we go from here? big_smile

#23 2012-11-26 09:44:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

Do you now see how this was done?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#24 2012-11-26 09:48:08

BarandaMan
Guest

Re: Really Difficult Differentiation! Help please!

bobbym wrote:

Hi;

Do you now see how this was done?

Yes bobbym I fully understand this now! Thank you!

#25 2012-11-26 09:50:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Really Difficult Differentiation! Help please!

Hi;

Can you differentiate this wrt Pi?

It is just a power rule.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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