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Calculus/Calculus derivative

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Expert: Alon Mandes - 8/11/2008


Question
Find dy/dx for y = x arc cos 2x

Answer
Finding derivatives of such kind, involves inversion :
If y=x*arc[cos(2x)] then y'=arc[cos(2x)]+x*arc[cos(2x)]'.
Let's calculate arc[cos(2x)]' : Suppose z=arc[cos(2x)] then
2x=cos(z), now let's perform derivative for both side with respect
to x , we gain : 2=-sin(z)*z' --> z'=-2/(sinz)=-2/sqrt(1-cosz^2).
z'=-2/sqrt(1-4x^2). So now we can claim that :
y'=arc(cos2x)- 2x/sqrt(1-4x^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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