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Calculus/Derivatives

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Expert: Alon Mandes - 3/4/2009


Question
What is the derivative of Y= secx/x and the derivative of y=cosx/1+sinx. Thanks,

Answer
y=(sec[x])/x
To derive y , we will follow these rules :
1. Sec[x]'=Sec[x]*Tang[x]
2. [f/g]'=[f'g-g'f]/g²
y'=( Sec[x]*Tang[x]*x-Sec[x] )/x² = Sec[x]( x*Tang[x]-1 )/x² =
(x*Sin[x]-Cos[x])/(xCos[x])² .

--------

y=Cos[x]/(1+Sin[x])
y'=( -Sin[x](1+Sin[x])-Cos[x]*Cos[x] )/(1+Sin[x])² =
( -Sin[x]-(Sin[x])²-(Cos[x])² )/(1+Sin[x])² =
( -Sin[x]-( (Sin[x])²+(Cos[x])² ) )/(1+Sin[x])² =
( -Sin[x]-1 )/(1+Sin[x])² =
-(1+Sin[x])/(1+Sin[x])² =
-1/(1+Sin[x]) .

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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