derivative of a negative exponential function

[Mickey]

The re-growth of a population of rabbits in an area is given by the function
P(t) = 500 divided by 1 + e^-t where t is the time in years. how can I determine the rate of growth in the population after 3 years. I know it is necessary to get the derivative of P(t) but and substitute in t =3 but I don't know how to get derivative of (1 + e^-t)^-1
Please help me.

 

[galactus]

\(\displaystyle \frac{d}{dt}\left[\frac{1}{1+e^{-t}}\right]\)

Quotient rule:

\(\displaystyle \frac{(1+e^{-t})(0)-(1)(-e^{-t})}{(1+e^{-t})^{2}}=\frac{e^{-t}}{(1+e^{-t})^{2}}\)

This seems like deja vu all over again. viewtopic.php?f=3&t=34161

 

[Deleted member 4993]

This seems like deja vu all over again. ...

Yep ... if you just observe - you can see lot of things.....