time derivative of a variable os inversly proportional to other variable

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April 28th 2010, 04:20 PM
lalleykhan

time derivative of a variable os inversly proportional to other variable

Hi,
I have the following question:

If the time derivative of a variable (A) is inversly proportional to some other variable (B), and we want a high variation in values of (B) values for different time steps, then should (A) be varying more or less?

Anyone, please reply. Thanks in advance
May 2nd 2010, 11:48 PM
CaptainBlack

Quote:

Originally Posted by lalleykhan

Hi,
I have the following question:

If the time derivative of a variable (A) is inversly proportional to some other variable (B), and we want a high variation in values of (B) values for different time steps, then should (A) be varying more or less?

Anyone, please reply. Thanks in advance

1. If you want help you should put more effort into making your question clear.

2. Lets assume you mean you have:

$B(t)=\frac{k}{A(t)}$

Then:

$B'(t)=-\frac{kA'(t)}{(A(t))^2}$

Now what were you asking again?

CB
May 3rd 2010, 12:38 AM
HallsofIvy

I would interpret "the time derivative of a variable (A) is inversly proportional to some other variable (B)" as meaning $\frac{dA}{dt}= \frac{k}{B}$ . But, then, that does NOT give any condition on the derivative of B so I suspect CaptainBlack's interpretation is the correct one.