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Calculus/Log functions

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Expert: Alon Mandes - 6/13/2008


Question
hey Chris i need some help with a problem i need to find f' and state the domains of f and f' for the following problem

lnlnln x

thanks a lot!

Answer
Hello Alvin
Let's calculate the derivative of f(x)=Ln(Ln(Lnx)) : As we know,
Ln(g(x))'=g'(x)/g(x). So f(x)'=[Ln(Lnx)]'/Ln(Ln(Lnx)). No we have
to find [Ln(Lnx)]' : we follow the same rule, we get :
[Ln(Lnx)]'=(1/x)/Lnx. thus f'(x)=[(1/x)/Lnx]/Ln(Ln(Lnx)), or
f'(x)=1/[xLn(x)*Ln(Ln(Lnx))].
The domain of f(x) is Ln(Lnx)>0. & that happens only when Lnx >1.
Lnx >1 means x>e.
the domain of f'(x) is Lnx >0 & Ln(Lnx)>0 which is also x>e.

Alon.  

Calculus

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Alon Mandes

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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 .

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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.

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M.A in Mathematics & Bs.c in Electronics.

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