Results 1 to 5 of 5

Math Help - derivative

  1. #1
    Newbie
    Joined
    Sep 2006
    From
    Chile
    Posts
    10

    Unhappy derivative

    Im supposed to find the derivative of the following two problems:

    (a) f(x) = |(x+2)/(x-3)|

    (b) f(x) = (1/(1+|x|))+(1/(1+|x-3|))

    I have to mention my teacher just havent bother to teach how to derive of the absolute value... so if any one can also explain that to me greatly apreciated...

    also if anything sounds weird im sorry but im talking math clases in spanish for the first time in long time.

    thanx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by sacwchiri View Post
    I have to mention my teacher just havent bother to teach how to derive of the absolute value... so if any one can also explain that to me greatly apreciated...
    The derivative of the function f=|x| is:
    1 if x>0
    -1 if x<0

    Note it is not differencialable at x=0.

    Another way to write the absolute value derivative is,
    x/|x|
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,820
    Thanks
    317
    Awards
    1
    Quote Originally Posted by sacwchiri View Post
    Im supposed to find the derivative of the following two problems:

    (a) f(x) = |(x+2)/(x-3)|

    (b) f(x) = (1/(1+|x|))+(1/(1+|x-3|))

    I have to mention my teacher just havent bother to teach how to derive of the absolute value... so if any one can also explain that to me greatly apreciated...

    also if anything sounds weird im sorry but im talking math clases in spanish for the first time in long time.

    thanx
    Consider y = |x|. This function is: {y = -x for x < 0 and y = x for 0<= x
    } This means the derivative of y is {y' = -1 for x < 0 and y' = 1 for 0 < x}. Note that the derivative of y is undefined for x = 0.

    My best advice is to write the function out in terms of its domains before you take the derivative. For example:

    f(x) = |(x+2)/(x-3)|

    Use the intervals: (-infinity, -2), (-2, 3), and (3, infinity).
    On (-infinity, -2) f(x) = -(x+2)/[-(x-3)] = (x+2)/(x+3)
    On (-2, 3) f(x) = (x+2)/[-(x-3)] = -(x+2)/(x-3)
    On (3, infinity) f(x) = (x+2)/(x-3)

    Now take the derivative of each of the expressions above. Again we have that the derivative of f(x) does not exist for x = -2, nor for x = 3.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Consider a differenciable function f(x) on the interval (a,b)

    What is the derivative of |f(x)|?

    To answer the question we use the chain rule,
    Thus,
    f'(x) if f(x)>0
    -f'(x) if f(x)<0

    And the zeros of f(x) on (a,b) do not make |f(x)| differenciable.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2006
    From
    Chile
    Posts
    10

    derivative

    thanx... this has been really helpfull
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 02:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  3. Replies: 2
    Last Post: November 6th 2009, 02:51 PM
  4. Replies: 1
    Last Post: January 7th 2009, 01:59 PM
  5. Fréchet derivative and Gâteaux derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 23rd 2008, 04:40 PM

Search Tags


/mathhelpforum @mathhelpforum