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Algebra problem. Help if you know anything of maths or biochemistry
    #14296551 -

Can someone explain to me where the following relationship comes from:

∂x/x=∂lnx

It has something to do with flux control coefficients in biochemistry but this formula means nothing to me. Could someone elaborate on that :grin:


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Edited by mellowparty (04/16/11 07:06 PM)

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Re: Mathematical help [Re: mellowparty]
    #14296703 -

It is talking about the derivative.  The ∂lnx (derivative of lnx with respect to x) is equal to (1/x)*∂x.  In other words, change in ln x is equal to change in x divided by x.

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Re: Mathematical help [Re: clintyclint]
    #14296734 -

Aren't those only partial derivatives though?

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Re: Mathematical help [Re: orangeyouglad]
    #14296745 -

can we have this in the johnny has five apples style please?

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Re: Mathematical help [Re: clintyclint]
    #14296749 -

So it has something to do with ∫x-1dx=lnx+C ?

Would it be correct to say that ∂lnx=dlnx/dx ?

Or is this a whole new concept?


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Re: Mathematical help [Re: chameleon303]
    #14296804 -

I don't really know what the formula means, but derivatives are usually d/dx. The sign for partial derivatives is ∂. I just recognize it from physics, I had a final yesterday so it's still fresh in my mind.

http://tutorial.math.lamar.edu/Classes/CalcIII/PartialDerivatives.aspx

I didn't read the entire thing, but the first bit explains it fairly well.

"Recall that given a function of one variable, the derivative represents the rate of change of the function as x changes.  This is an important interpretation of derivatives and we are not going to want to lose it with functions of more than one variable.  The problem with functions of more than one variable is that there is more than one variable.  In other words, what do we do if we only want one of the variables to change, or if we want more than one of them to change?  In fact, if we’re going to allow more than one of the variables to change there are then going to be an infinite amount of ways for them to change.  For instance, one variable could be changing faster than the other variable(s) in the function.  Notice as well that it will be completely possible for the function to be changing differently depending on how we allow one or more of the variables to change."

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Re: Mathematical help [Re: orangeyouglad]
    #14302096 -

So if ∂x/x=∂lnx then does that mean ∂x/x=∂[∫x-1dx-C] where ∫x-1dx=lnx+C ? :uhoh:

I assume not.

I'll try to put the problem in its original context

Basically it has to do with a flux coefficient (CJ) that gives an indication of the influence of a given enzyme in a pathway on the overall flux of pathway. The flux (J) is the amount of substrate converted per given amount of time. So the flux coefficient is equal to

CJ= (∂J/J) / (∂[E]/[E]) = ∂lnJ / ∂ln[E] ≈ (ΔJ/J) / (Δ[E]/[E])    where [E] is the enzyme concentration

So a small flux coefficient means that high changes in [E] would not affect the pathway flux significantly and vice versa ie how important is this enzyme in terms of flux regulation.

:drugnerd: anyone?


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Re: Mathematical help [Re: mellowparty]
    #14302226 -

i fucking wish i knew what you guys are talking about. What class is this for, mellow?


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want a cool color changing shroom gif that is easy on the eyes for YOUR shroomery background? 3 easy steps <-- click here

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Re: Mathematical help [Re: realfuzzhead]
    #14302238 -

Control of metabolism. Its not my cup of tea but its biochemistry so I dont hate it.


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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: mellowparty]
    #14302256 -

mellowparty said:
Can someone explain to me where the following relationship comes from:

∂x/x=∂lnx

It has something to do with flux control coefficients in biochemistry but this formula means nothing to me. Could someone elaborate on that :grin:


basically what that says it that the function y=1/x which is really just x to the power of negative one
well that function y=1/x has a rate of change equal to the function y=lnx which is really just e to the power of y which equals x
so if you want to know the instaneous rate of change of the function y=1/x you just need to find out the corresponding y value on the function y=lnx
So looking at this graph


lets say you wanted to know the instantenous rate of change of the function y=1/x when x=e for example so then you look at the derivative function which is y=lnx

well if you substitute e for x you get y=lne and well thats of course just 1. So basically the function y=1/x is increasing by one unit for every unit you increase x


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THE MOUTH OF THE VOID IS GOD-WIDE

THE EYE OF THE CREATOR IS VOID-WIDE

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: sunset_mission]
    #14302301 -

Most likely I'm slow-ish but that sounds like y=x-1 and its first derivative is dy/dx=lnx.

So my question is how does ∂ differ from d thats found in dy/dx?


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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: mellowparty]
    #14302353 -

∂ is used in partial derivatives.  If you have for example

f(x,y) = x^2 + 4y^4, then ∂f(x,y)/∂y = 16y^3 - when there's multiple variables you don't use d you use ∂

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: mellowparty]
    #14302359 -

mellowparty said:
Most likely I'm slow-ish but that sounds like y=x-1 and its first derivative is dy/dx=lnx.

So my question is how does ∂ differ from d thats found in dy/dx?


∂ is just delta used in place of d which refers to differentiate


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THE MOUTH OF THE VOID IS GOD-WIDE

THE EYE OF THE CREATOR IS VOID-WIDE

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: mellowparty]
    #14302417 -

mellowparty said:
Most likely I'm slow-ish but that sounds like y=x-1 and its first derivative is dy/dx=lnx.

So my question is how does ∂ differ from d thats found in dy/dx?


I've never seen that symbol before, and I've passed a college level Calculus II class.

Anywho, the first derivative of x^(-1) is not ln(x).  ln(x) would be the anti-derivative of x^-1.


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"You can peel it [language] off the ceiling and make it dance in front of you" - McKenna

<3 .

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: Cynosure]
    #14302430 -

pwnasaurus said:
∂ is used in partial derivatives.  If you have for example

f(x,y) = x^2 + 4y^4, then ∂f(x,y)/∂y = 16y^3 - when there's multiple variables you don't use d you use ∂


sweet

Man I love the shroomery, it delivers answers to all of my problems :vaped::thumbup:

So in my problem which was

CJ= (∂J/J) / (∂[E]/[E]) = ∂lnJ / ∂ln[E] ≈ (ΔJ/J) / (Δ[E]/[E])


basically I use partial derivatives for the flux and enzyme conc. which appear to be interrelated in a multivariable function.
Cynosure said:
mellowparty said:
Most likely I'm slow-ish but that sounds like y=x-1 and its first derivative is dy/dx=lnx.

So my question is how does ∂ differ from d thats found in dy/dx?


I've never seen that symbol before, and I've passed a college level Calculus II class.

Anywho, the first derivative of x^(-1) is not ln(x).  ln(x) would be the anti-derivative of x^-1.


yeah I think I got confused on this one

The integral of x-1 with respect to x is going to be lnx+C therefore the derivative of lnx with respect to x will be 1/x.


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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: Cynosure]
    #14302440 -

Cynosure said:
I've never seen that symbol before, and I've passed a college level Calculus II class.




it was Newton in the early 1700's who started to use delta for derivatives


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THE MOUTH OF THE VOID IS GOD-WIDE

THE EYE OF THE CREATOR IS VOID-WIDE

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: sunset_mission]
    #14302453 -

sunset_mission said:
Cynosure said:
I've never seen that symbol before, and I've passed a college level Calculus II class.




it was Newton in the early 1700's who started to use delta for derivatives


That would explain it.  I haven't taken physics since high school.


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"You can peel it [language] off the ceiling and make it dance in front of you" - McKenna

<3 .

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Re: Algebra problem. Help if you know anything of maths or biochemistry [Re: sunset_mission]
    #14302455 -

I did calculus for fun last summer. We never covered integration in highschool and I spent a significant portion of my summer sat at home watching youtube videos and reading on how to solve calculus problems and apply them to stuff like radioactive decay.


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