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Expert: Alon Mandes - 8/7/2009


Question
Find the answer using composite rule first?
f(x)=In(1-e^-x) (i.e. 1 - e to the power of -x) (x>0)
find the f'(x) using composite rule and find second derivatives i.e.f''(x) using Quotient rule only...
4 hours ago - 4 days left to answer.
Additional Details
that's what i get but my options are

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

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

3)e^x/e^x-1

4)1/e6x-1

5)2e^x/(e^x+1)^2

6)- ((2e^x)/(e^x-1)^2)
7)- ((e^x)/(e^x-1)^2))
8) -(1/(e^x-1)^2)


Answer
f(x)=Ln[1-e^(-x)]
v=-x & u=1-e^(v) . Thus :
1. v'=-1
2. u'=-e^(v)*v'=e^(-x)
Therefore :
f=Ln(u)
f'=u'/u=e^(-x)/[1-e^(-x)]

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

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".

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

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

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