What is the second derivative of a logistic differential ...

[Sandstorm]

I can manage integrating it, but how to I take the second derivative?

I have a partial formula written down, but it's incorrect.

Thanks!

[coco]

This is the original equation below:
X(t) = (1 + ( (1/x) -1)e^(-rt) ) ^-1

Solve the denominator :
X(t) = (1 + ( (1 - x)/x)e^(-rt) ) ^-1

Solve for the lowest denominator and bring to the numerator
X(t) = X(X + e^(-rt) - Xe^(-rt) ) ^-1

Now take the first derivative:
X'(t) = -X(-re^(-rt) + Xre^(-rt) ) ^-2

Then take the second derivative
X''(t) = 2X(r^2e^(-rt) - Xr^2e^(-rt) ) ^-3

Make the equation into a nice form:
X''(t) = 2X/(r^2e^(-rt) - Xr^2e^(-rt) )^3

You may go ahead to seperate common variables but the most important point is about the mastery of the concept.

I hope this helps.