# time derivative of a variable os inversly proportional to other variable

• Apr 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?

• 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?

2. Lets assume you mean you have:

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

Then:

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

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 $\displaystyle \frac{dA}{dt}= \frac{k}{B}$. But, then, that does NOT give any condition on the derivative of B so I suspect CaptainBlack's interpretation is the correct one.