Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quicky on derivative of absolute value in exponential

  1. May 10, 2008 #1
    Hey folks,

    I'm looking for a little guidance in solving the derivative y'(x)of the following function containing an absolute in the exponent:


    I'm pretty sure its not as simple as

    [tex]y'(x)=a e^{a|x|}[/tex]

    Any suggestions??
  2. jcsd
  3. May 10, 2008 #2
    i think the problem is that [tex] |x| [/tex] is not differential in zero so, [tex]e^{a|x|}[/tex] is not differential in zerp, so if you want to calculate the differential somewhere else, then just do in the two cases. Then you get for [tex]x<0[/tex]

    [tex]\partial_x e^{a|x|} = \partial_x e^{-ax} = -ae^{-ax} [/tex]

    for [tex]x>0[/tex] you get

    [tex]\partial_x e^{a|x|} = \partial_x e^{ax} = ae^{ax} [/tex]

    combining these could be

    [tex]\partial_x e^{a|x|} = sign(x) a e^{a|x|} = \frac{x}{|x|} a e^{a|x|}[/tex]

    but remember that it is not defined in 0.
  4. May 10, 2008 #3

    so the [tex]\frac{x}{|x|}[/tex] is really just a neat way of setting the coefficient to [tex]\pm 1[/tex], depending on where x is.

    Thats cool. :)

    Thanks mranderson, very helpful.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Quicky on derivative of absolute value in exponential