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) ] / [1e^x]^4
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