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Calculus/successive derivaties

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Expert: Alon Mandes - 11/12/2009


Question
find d^y/dx^2 for the following functions
1) xy+2y=5x

2)x^2+y^2+a^2

3)x^3+y^3= a^3

Answer
1) d/dx { xy+2y } = d/dx {5x}
y+xy'+2yy'=5
y+y'(x+2y)=5
y'=(5-y)/(x+2y)
 d/dx { y+xy'+2yy' } = d/dx {5}
y'+y'+xy''+2yy''+2y'^2=0
2y'+2y'^2+y''(x+2y)=0
y''=-2(y'+y'^2)/(x+2y)

2) d/dx {x^2+y^2} = d/dx {a^2}
2x+2yy'=0
y'=-x/y
d/dx {x+2yy'} =d/dx {0}
1+2yy''+2y'^2=0
y''=-(1+2y'^2)/2y

3)d/dx {x^3+y^3} = d/dx {a^3}
3x^2+3y'y^2=0
y'=-x^2/y^2
d/dx {x^2+y'y^2} = d/dx {0}
2x+2yy'^2+y''y^2=0
y''=-(2x+2yy'^2)/y^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".

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

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

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