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Question
if f = (1+x)^1/2/(1-x)^1/2 find dy / dx
(1+x)^(1/2)
y= -----------
(1-x)^(1/2)
The rule determine : [f/g]'=(f'g-g'f)/(g^2) . Therefore :
[(1+x)^(1/2)]' * [(1-x)^(1/2)] - [(1+x)^(1/2)] * [(1-x)^(1/2)]'
y' = ----------------------------------------------------------------
[ (1-x)^(1/2) ]^2
[(1/2)(1+x)^(-1/2)] * [(1-x)^(1/2)] + [(1+x)^(1/2)] * [(1/2)(1-x)^(-1/2)]
y' = ----------------------------------------------------------------------------
(1-x)
(1-x+1+x)
---------------------------------------------------------------------
2[(1+x)^(1/2)][(1-x)^(1/2)]
y' = ----------------------------------------------------------------------------
(1-x)
1
y'=-----------------
(x-1)(1-x^2)^(1/2)
Alon.
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Answers by Expert:
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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