Math

posted by .

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

  • Math -

    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 -

    I solved it ! but I have different solution!!

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM?
  2. Derivatives- Math

    Can someone explain how to find the derivative of : 1. y= 5^ãx / x And the second derivative of: y= xe^10x For this question I got up to the first derivative and got this y = e^10x + 10xe^10x but I can't seem to get the correct …
  3. calculus

    Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and …
  4. calculus

    Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the second …
  5. Calculus

    I need to find the second derivative of y=x(x-1)^1/2. I found the first derivative is 2x-1/2(x-1)^1/2, if someone could check, but I am miserably stuck on the second derivative.
  6. Calc-please help!

    What is the second derivative of (x^3)/(x^2-1)?
  7. CALCULUS HELP

    Find the second derivative for the function 5x^3+60x^2-36x-41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative …
  8. Applied Calculus

    Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first …
  9. Calc I

    if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t-1)^-1/2 * 4t^3 and i'm trying to figure out if i need the product rule again to find the second derivative -1t^3(4t-1)^-3/2 * 4t^3 The answer if -4/27 and I'm …
  10. math

    For what intervals is g(x) = 1/x2 + 1 concave down?

More Similar Questions