Posted by **008** on Sunday, February 3, 2013 at 8:23am.

What is the second derivative for [f(x) = 1/(1+e^-x)]?

- Math -
**Reiny**, Sunday, February 3, 2013 at 9:00am
I have just answered a question on this same function when you posted as "009".

Keep the same name please.

In this case I will simplify the function a bit

f(x) = 1/(1 + e^-x) = (1+e^-x)^-1 * e^x/e^x

= e^x/(e^x + 1)

f ' (x) = ( (e^x + 1)(e^x) - (e^x)(ex) )/(e^x + 1)^2

= e^x/(e^x + 1)^2

f '' (x) = ( (e^x + 1)^2 (e^x) - (e^x)(2)(e^x + 1)(e^x) )/(e^x + 1)^3

I will leave it up to you to simplify the top

- Math -
**008**, Sunday, February 3, 2013 at 10:51am
I solved it ! but I have different solution!!

f''(x) =[ (-e^-x)(1+2e^-x) ] / [1-e^-x]^4

## Answer this Question

## Related Questions

- Derivatives- Math - Can someone explain how to find the derivative of : 1. y= 5...
- Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...
- Calc-please help! - What is the second derivative of (x^3)/(x^2-1)? And how ...
- calculus - Please help with this. I need the first derivative of f(x)=4(x+...
- Calculus - R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I ...
- Calc I - if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t...
- calculus - Please help with this. I submitted it below and was asked to clarify ...
- Applied Calculus - Find the first and second derivative of the function: x/(7x+...
- CALCULUS HELP - Find the second derivative for the function 5x^3+60x^2-36x-41 ...
- Calculus - How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 ...