Partial Derivative Log

KarimAzer · 2011-11-08 01:52:59

How does this work?

If I wanted to differentiate x1logx2, would it give me logx2 (wrt x1) and x1/x2(wrt x2)?

Is that correct or should I use the product rule? Thanks

Bob · 2011-11-08 01:58:04

hi KarimAzer

Provided x1 and x2 are independent variables then your partial differentiations are correct. No need for the product rule.

Slight complication if that log is not to base e.

Bob

KarimAzer · 2011-11-08 01:58:25

The way I'm doing it so x1logx2 with respect to x1;

differentiating gives (1*logx2)+(0) = logx2

differentiating wrt x2 gives (0*logx2)+ (x1/x2) = x1/x2

Where am I going wrong?

KarimAzer · 2011-11-08 01:59:53

Thank you for your reply!

Yeah it is the natural log! But my teacher likes to write it as log, sometimes I press log instead of ln on the calculator by mistake still though...

KarimAzer · 2011-11-08 02:05:35

Am I right in assuming after this, that if I differentiated logx2 with respect to x1, it would be 0? Not 1?

I really get confused when to input the values

bobbym · 2011-11-08 03:20:45

Hi KarimAzer;

Are you saying differentiate a function of one variable with respect to another one? if so, that would be like differentiating a constant. That would be 0.

KarimAzer1 · 2011-11-09 12:31:15

bobbym wrote:

Hi KarimAzer;
Are you saying differentiate a fumction of one variable with respect to another one? if so, that would be like differentiating a constant. That would be 0.

Thank you! I thought it must be...darn logs.

My problems seem to be getting easier as I get more idiotic....

I've got a much simpler problem that I'm trying to just simply...

I have

(nx/n+10) - x

It doesn't equal 0, I'm just trying to simplify that term itself. I put it into brackets like this x((n/n+10) - 1) but couldn't get any further? Could someone help me?

Similarly, the previous problem I got down to x((n+1)/n)-1) and that was easy to simplify down to x/n ..... and this was the correct solution...

Why can't I simplify that simple thing...I do one right and get stuck on the other!

bobbym · 2011-11-09 12:33:19

Hi;

Is this what you are working on?

My problems seem to be getting easier as I get more idiotic....

I think as you progress you will examine fundamental concepts. These appear simple and easy but are not. I am afraid the more you know the more idiotic your errors will seem to you.

KarimAzer1 · 2011-11-09 12:41:10

NOONE ANSWER IT! I did the initial algebra wrong..i'll post new thread thanks all

bobbym · 2011-11-09 12:44:01

Hi;

Okay, think about it and post when it is clear in your mind.

KarimAzer1 · 2011-11-09 12:45:38

bobbym wrote:

Hi;
Is this what you are working on?
My problems seem to be getting easier as I get more idiotic....
I think as you progress you will examine fundamental concepts. These appear simple and easy but are not. I am afraid the more you know the more idiotic your errors will seem to you.

Your too fast! Thank you

I apologize for wasting your time, I'm struggling.

I think what I want to break down is; x(((n-1)/(n+10)) - 1 )

I need to break that down into a very simple term like n/x or x/n...

If you look at my previous example, ( the way I did it was my putting numbers in to as n ) and manipulating the algebra until it worked, then applied it to the general. But for this, I don't know how to manipulate ((n-1)/(n+10)) so that I can break it down....

KarimAzer1 · 2011-11-09 12:46:37

bobbym wrote:

Hi;
Okay, think about it and post when it is clear in your mind.

Ok, don't reply to the above then ^^. I'll try and use latex so it isn't constantly in this horrific computer form.

KarimAzer1 · 2011-11-09 12:54:51

x(

)

I know that looks weird, but I mean x* (all of the stuff in latex) i.e. x(n-1)/n+10 - x (essentially).

As I spoke of the previous example x(

) i.e. x(n+1)/n - x

But it seems to work if I take the x outside the bracket...it's the correct method according to this book.

So in the example I did correct, I got essentially had x* (((n+1)/n) - 1)

((n+1)/n)-1 = (n/n)+(1/n)-1 = 1+(1/n)-1 = (1/n). Multiplying by the x in the above line givens x/n.

But with my expression in my example, I can put x on the outside of the bracket, but don't know how to manipulate it on the inside.

I hope that makes more sense?

bobbym · 2011-11-09 13:07:35

Hi;

You can use this page to latex your work perfectly. It has pull down menus so it is easier

http://latex.codecogs.com/editor.php

This is what you are working on?

I am not totally clear on what you want to do with it. Can you describe using the latex editor I have mentioned?

KarimAzer1 · 2011-11-09 13:17:38

The website only allows me to download it? How do I upload it afterwards?

What you've written is correct.

I'm evaluating biasedness of a sample mean, so what you've just posted is equal to 'the bias of the sample mean'

That's what I meant by it can't be equated to 0.

With the equation, I need to somehow manipulate it so that it becomes n/x or x/n, or something a lot simpler so that I can give a simple response about whether or not the sample mean is biased.

I know my 'example' is really unstructured how I've written it, but it's correct and I manipulated the formula down and I'm applying the same logic but with this example it's just not working.

bobbym · 2011-11-09 13:25:47

Hi;

The website only allows me to download it? How do I upload it afterwards?

You should see a big input box on that page. It will have the latex form for your expressions that you make from the menus. Just copy it and paste it over here.

KarimAzer1 · 2011-11-10 00:09:21

I want to manipulate that formula, I want it to be broken down.

For example, on the last part I had

And for that; I used some examples to break it down. E.g if n=4; (5/4)-1 = 0.25.

So as my check I knew when I was breaking it down, I needed it to answer 0.25 when n=4.

So eventually I got to this;

=

(Which is equal to

= 0.25, so my check is complete)

I can eliminate the n's and the '-1' and be left with

= x/n.

This is exactly what I'm trying to do with the figure at the top of my page. I really can't think of how to manipulate it to break it down further.

I hope this is much clearer now bobby, thank you for your continued help; I'm going to keep trying since I think we have a lot of time difference. I'll post if I get the answer.

bobbym · 2011-11-10 00:23:36

Hi;

KarimAzer1 · 2011-11-10 00:38:00

bobbym wrote:

Hi;

Thank you! The first one is so much easier for me.... I have no idea how did you get to the second expression? Thank you for helping me

bobbym · 2011-11-10 00:43:50

Hi;

From the rule of fractions:

We start by putting the problem into that form:

Applying the rule:

KarimAzer1 · 2011-11-10 00:50:54

Thank you bobby, really thank you I am so bad! But at least I try

KarimAzer1 · 2011-11-10 00:52:04

bobbym wrote:

Hi;
From the rule of fractions:
We start by putting the problem into that form:
Applying the rule:

You really have helped, I guess in Algebra they use everything even if it's not the topic on it, they can apply every rule!

bobbym · 2011-11-10 00:59:38

Hi;

I guess in Algebra they use everything even if it's not the topic on it, they can apply every rule!

If you learned that fact then you have made a gigantic jump in your understanding! Took me a long time to get out of the box my schooling put me into. I thought all answers to all problems were 1,2,3,4, √2, √3, 1/2, and 1/3 because that is all I ever saw in class. First time I saw a decimal answer like .1465243 I could not understand it! I had to quit my ambitions of being a chemist because of that!

KarimAzer1 · 2011-11-10 01:03:32

bobbym wrote:

Hi;
I guess in Algebra they use everything even if it's not the topic on it, they can apply every rule!
If you learned that fact then you have made a gigantic jump in your understanding! Took me a long time to get out of the box my schooling put me into. I thought all answers to all problems were 1,2,3,4, √2, √3, 1/2, and 1/3 because that is all I ever saw in class. First time I saw a decimal answer like .1465243 I could not understand it! I had to quit my ambitions of being a chemist because of that!

They really do narrow it early on so it makes everything harder more daunting! Hehe...I still don't understand that decimal .

That's awful , I'm sure you would make a great chemisty

bobbym · 2011-11-10 01:13:20

It is water under the bridge now. I eventually got smarter, no one stays an idiot for more than 4 or 5 decades.

Math Is Fun Forum

#1 2011-11-08 01:52:59

Partial Derivative Log

#2 2011-11-08 01:58:04

Re: Partial Derivative Log

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