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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

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