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Derivative of |x|

  1. Jan 19, 2010 #1

    Char. Limit

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    Is this: [tex]\frac{d |x|}{dx}[/tex] equal to the unit step function?

    Also, is the unit step function equal to [tex]y=\frac{|x|}{x}=\frac{x}{|x|}[/tex]?
     
  2. jcsd
  3. Jan 19, 2010 #2

    George Jones

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    No.

    For [itex]x < 0[/itex], what is [itex]d \left| x \right| /dx[/itex]?

    For [itex]x > 0[/itex], what is [itex]d \left| x \right| /dx[/itex]?
     
  4. Jan 19, 2010 #3

    Char. Limit

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    For x<0, the derivative is -1. For x>0, the derivative is +1.

    Oh, that's not the unit step function, is it? Is there a "function" with those properties?
     
  5. Jan 19, 2010 #4

    cronxeh

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  6. Jan 19, 2010 #5

    jgens

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    The sign function probably comes the closest but it's defined at [itex]x = 0[/itex] while the derivative of [itex]|x|[/itex] is not. But if you're interested, here's a brief discussion about it: http://en.wikipedia.org/wiki/Sign_function
     
  7. Jan 19, 2010 #6

    Char. Limit

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    I am interested.

    Thanks for the help. I figured that the derivative was either abs(x)/x or x/abs(x), but I couldn't remember if such a function had a name. All I could think of was the unit step function (it looked like a step to me).

    Does the sign function have a great use in mathematics other than being interesting?
     
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