Math Is Fun Forum

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

sgn(x)!!!

hi guys

i was wondering what derivatives of |x| and sgn(x) are.i thought of something but i got that they were sgn(x) and 0 respectfully.i think something is wrong here.What?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: sgn(x)!!!

hi Stefy,

Haven't 'spoken' to you in a while.  Hope you are well.   

Derivatives have to be 'well defined'.  Specifically, this breaks down where the left limit isn't the same as the right limit.

So neither have a  defined value at x = 0.

For |x|           the deriv = 1 for x > 0       and         -1 for x < 0.

How are you defining sgn(x) ?

If you mean         1 when x > 0         and          -1 when X < 0,         then zero is correct. 

As this function is discontinuous at x = 0,   I think you must exclude x = 0 from this derivative even though the value is the same either side of zero.

Bob

Last edited by Bob (2011-11-11 20:45:55)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: sgn(x)!!!

hi bob

yes,i have been occupied by school and my subjects.this was a crazy week.i'm glad it's over,but there is next week exams and i have physics, analysis and in the one after i have geometry and programming. very busy weeks!

anyway,if i gave the restriction x<>0 then would my answers be correct?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: sgn(x)!!!

hi Stefy

Yes, that's what I think.

Good luck in the exams (not that you need it .. I'm sure you'll do brilliantly)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: sgn(x)!!!

ok thanks for the help,and could sure use luck!I'm not sure about that brilliantly!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

Re: sgn(x)!!!

i was wondering what derivatives of |x| and sgn(x) are.
i thought of something but i got that they were sgn(x) and 0
respectfully.i think something is wrong here.What?

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: sgn(x)!!!

nice explanation! thanks rya!

i guess sgn(x) can be done similairly.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

zetafunc.

Guest

Re: sgn(x)!!!

i was wondering what derivatives of |x| and sgn(x) are.
i thought of something but i got that they were sgn(x) and 0
respectfully.i think something is wrong here.What?

Sorry for the bump, but could you not just say

?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: sgn(x)!!!

That looks ok too.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.