Results 1 to 5 of 5

Math Help - Derivativ eo asbolute value

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    178

    Derivativ eo asbolute value

    y= \mid{x\mid}^2
     y= \sqrt{x^2}^2
     2 \sqrt{x^2}*\frac{1}{2 sqrt(x^2)}*2x
    \frac{4x*sqrt(x^2)}{2*sqrt(x^2)} - how does the LaTex work with this?
    where \mid{x\mid}^2 = \sqrt{x^2}^2
    I got 2x.
    This seems too simplified. Does it really simplify that much? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by Truthbetold View Post
    y= \mid{x\mid}^2
     y= \sqrt{x^2}^2
     2 \sqrt{x^2}*\frac{1}{2 sqrt(x^2)}*2x
    \frac{4x*sqrt(x^2)}{2*sqrt(x^2)} - how does the LaTex work with this?
    where \mid{x\mid}^2 = \sqrt{x^2}^2
    I got 2x.
    This seems too simplified. Does it really simplify that much? Thanks!
    Hello,

    surprising, isn't it? But you are right:

    Use the definition of the absolute value:

    | x | =\left \{ \begin{array}{lr}x, & x > 0 \\0, & x = 0\\-x, &x < 0\end{array}\right.

    Now take your function:

    y = | x |^2 = \left \{ \begin{array}{lr}x^2, & x > 0 \\0, & x = 0\\(-x)^2 = x^2, &x < 0\end{array}\right. which will give the derivation y' = 2 \cdot | x | = \left \{ \begin{array}{lr}2x, & x > 0 \\0, & x = 0\\2 \cdot (-x) \cdot (-1), &x < 0\end{array}\right.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Hmm.. Isn't {|x|}^2 = x^2 anyway?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by wingless View Post
    Hmm.. Isn't {|x|}^2 = x^2 anyway?
    in fact, you are correct..
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by Truthbetold View Post
    \frac{4x*sqrt(x^2)}{2*sqrt(x^2)} - how does the LaTex work with this?
    just put a \ before sqrt..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivativ
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 7th 2008, 03:54 AM

Search Tags


/mathhelpforum @mathhelpforum