Results 1 to 2 of 2

Math Help - Derivatives involving absolute values

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    83

    Derivatives involving absolute values

    Hey,

    I am slowly moving through the calculus portion of a math textbook my girlfriend lent me and am stuck on a few problems involving finding the first derivative of equations involving absolute values.
    I will use one of these as an example.

    Question
    Find the derivative of: y = \frac{ln|x|}{x^4}

    Solution
    Normally, if there was no absolute value, I would rewrite the equation as  (lnx)(x^{-4}) . Then I would use the product rule to get  (\frac{1}{x})(x^{-4}) + (-4x^{-5})(lnx) . Likely ending up writing it as  \frac {x}{x^4} + \frac {-4lnx}{x^5} .
    *I did this to show that I know how to do it with no absolute value*

    I know what an absolute value is, I am unsure of what to do with it when trying to derive a function that has one.
    I searched google and found a couple websites that tried to explain it, but I could not grasp what they were saying. I was hoping that someone could, using my example, explain (in english) how to go about doing this.
    Thanks in advanced!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    The reason the absolute value is given in the question is simply because the logarithm of a negative number does not exist. So, you should write your answer as:

    (\frac{1}{x})(x^{-4})+(-4x^{-5})(ln|x|)

    \frac {1}{x^5}-\frac {4}{x^5}ln|x|

    Hope that helps!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit involving absolute values
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 8th 2009, 05:36 AM
  2. Derivatives of Absolute Values?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 24th 2009, 01:45 AM
  3. Replies: 7
    Last Post: February 19th 2009, 07:11 PM
  4. Integers involving absolute values
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 19th 2008, 04:35 AM
  5. Limit involving Absolute Values.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 10th 2008, 10:24 AM

Search Tags


/mathhelpforum @mathhelpforum