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Calculus/Exonential differentiation

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Expert: Alon Mandes - 9/20/2010


Question
What are the first and second derivatives of this sigmoidal equation)
y = a + (b/(1 + e^x))

Answer
               b
y = a + -----------
              1 + e^x

             be^x
y' = 0 - --------------
         ( 1 + e^x )²

      be^x * ( 1 + e^x )² - [2e^x*(1 + e^x)]*[be^x]
y'' = ----------------------------------------------- =
                  ( 1 + e^x )^4

      be^x*(1+e^x)*[1+e^x-2e^x]      be^x*(1+e^x)*[1-e^x]
    ----------------------------  =  ---------------------- =
          ( 1 + e^x )^4              ( 1 + e^x )^4

    be^x*[1-e^(2x)]
    ---------------
    ( 1 + e^x )^4

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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