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Calculus/derivatives of log func.

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Expert: Alon Mandes - 5/28/2009


Question
How do I do these as well??? For both i need to find dy/dx.

We were only taught 1 example in class so I can't figure out how to do this...

problem is:

y=ln((3x-11)/(x(^5sqrt(x^2+1)))

The sqrt is 1/5.. not 1/2.. i didn't know how to write it in.

the second problem is:

y=x^(cos(x))

Answer
y = Ln[ (3x-11) / x*(x^2+1)^(1/5) ]
y = Ln[3x-11] - Lnx + (1/5)Ln[x^2+1]
y'/y = 3/(3x-11) - (1/x) + (1/5)2x/(x^2+1)
y' = Ln[(3x-11)/x*(x^2+1)^(1/5)]*[3/(3x-11)-(1/x)+(1/5)2x/(x^2+1)].

------------------------------------

y=x^cosx
Lny=cosx*Lnx
y'/y = (-sinx)*Lnx + cosx/x
y'=[x^cosx][cosx/x - sinxLnx] .

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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