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Question
What is the derivative of modulus of x with respect to x?
f(x)=|x| . Let's write it in different form :
| +x if x>0
f(x)=| -x if x<0
| 0 if x=0
To find derivative , we calculate the sided limits :
f'(x+)= lim [ f(x+h)-f(x) ]/h
h->0+
= lim [x+h-x]/h = 1
h->0+
f'(x-)= lim [ f(x+h)-f(x) ]/h
h->0-
= lim [-x-h+x]/h = -1
h->0+
We got :
f'(x+) ≠ f'(x-)
Thus, the derivative doesn't exist !
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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